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## ‣ O uso de ondaletas em modelos FANOVA; Wavelets FANOVA models

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em 20/10/2011
Português

Relevância na Pesquisa

47.746934%

#Wavelets (Matemática)#Análise de variância funcional#Teste de hipótese não paramétrico#Erros correlacionados (Estatística)#Estatística matemática#Wavelets (Mathematics)#Functional analysis of variance#Nonparametric hypothesis testing#Correlated errors (Statistics)#Mathematical statistics

O problema de estimação funcional vem sendo estudado de formas variadas na literatura. Uma possibilidade bastante promissora se dá pela utilização de bases ortonormais de wavelets (ondaletas). Essa solução _e interessante por sua: frugalidade; otimalidade assintótica; e velocidade computacional. O objetivo principal do trabalho é estender os testes do modelo FANOVA de efeitos fixos, com erros i.i.d., baseados em ondaletas propostos em Abramovich et al. (2004), para modelos FANOVA de efeitos fixos com erros dependentes. Propomos um procedimento iterativo tipo Cocharane-Orcutt para estimar os parâmetros e a função. A função é estimada de forma não paramétrica via estimador ondaleta que limiariza termo a termo ou estimador linear núcleo ondaleta. Mostramos que, com erros i.i.d., a convergência individual do estimador núcleo ondaleta em pontos diádicos para uma variável aleatória com distribuição normal implica na convergência conjunta deste vetor para uma variável aleatória com distribuição normal multivariada. Além disso, mostramos a convergência em erro quadrático do estimador nos pontos diádicos. Sob uma restrição é possível mostrar que este estimador converge nos pontos diádicos para uma variável com distribuição normal mesmo quando os erros são correlacionados. O vetor das convergências individuais também converge para uma variável normal multivariada.; The functional estimation problem has been studied variously in the literature. A promising possibility is by use of orthonormal bases of wavelets. This solution is appealing because of its: frugality...

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## ‣ Inferência estatística para regressão múltipla h-splines; Statistical inference for h-splines multiple regression

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em 14/04/2014
Português

Relevância na Pesquisa

49.07029%

#Modelos aditivos generalizados#Spline#Teoria do#Métodos MCMC#Testes de hipóteses estatísticas#Análise de regressão#Generalized additive models#Spline theory#MCMC methods#Statistical hypothesis testing#Regression analysis

Este trabalho aborda dois problemas de inferência relacionados à regressão múltipla não paramétrica: a estimação em modelos aditivos usando um método não paramétrico e o teste de hipóteses para igualdade de curvas ajustadas a partir do modelo. Na etapa de estimação é construída uma generalização dos métodos h-splines, tanto no contexto sequencial adaptativo proposto por Dias (1999), quanto no contexto bayesiano proposto por Dias e Gamerman (2002). Os métodos h-splines fornecem uma escolha automática do número de bases utilizada na estimação do modelo. Estudos de simulação mostram que os resultados obtidos pelos métodos de estimação propostos são superiores aos conseguidos nos pacotes gamlss, mgcv e DPpackage em R. São criados dois testes de hipóteses para testar H0 : f = f0. Um teste de hipóteses que tem sua regra de decisão baseada na distância quadrática integrada entre duas curvas, referente à abordagem sequencial adaptativa, e outro baseado na medida de evidência bayesiana proposta por Pereira e Stern (1999). No teste de hipóteses bayesiano o desempenho da medida de evidência é observado em vários cenários de simulação. A medida proposta apresentou um comportamento que condiz com uma medida de evidência favorável à hipótese H0. No teste baseado na distância entre curvas...

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## ‣ A Computationally Efficient Hypothesis Testing Method for Epistasis Analysis using Multifactor Dimensionality Reduction

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em /01/2009
Português

Relevância na Pesquisa

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Multifactor dimensionality reduction (MDR) was developed as a nonparametric and model-free data mining method for detecting, characterizing, and interpreting epistasis in the absence of significant main effects in genetic and epidemiologic studies of complex traits such as disease susceptibility. The goal of MDR is to change the representation of the data using a constructive induction algorithm to make nonadditive interactions easier to detect using any classification method such as naïve Bayes or logistic regression. Traditionally, MDR constructed variables have been evaluated with a naïve Bayes classifier that is combined with 10-fold cross validation to obtain an estimate of predictive accuracy or generalizability of epistasis models. Traditionally, we have used permutation testing to statistically evaluate the significance of models obtained through MDR. The advantage of permutation testing is that it controls for false-positives due to multiple testing. The disadvantage is that permutation testing is computationally expensive. This is in an important issue that arises in the context of detecting epistasis on a genome-wide scale. The goal of the present study was to develop and evaluate several alternatives to large-scale permutation testing for assessing the statistical significance of MDR models. Using data simulated from 70 different epistasis models...

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## ‣ Multiple Hypothesis Testing for Experimental Gingivitis Based on Wilcoxon Signed Rank Statistics

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em 01/05/2011
Português

Relevância na Pesquisa

48.567773%

Dental research often involves repeated multivariate outcomes on a small number of subjects for which there is interest in identifying outcomes that exhibit change in their levels over time as well as to characterize the nature of that change. In particular, periodontal research often involves the analysis of molecular mediators of inflammation for which multivariate parametric methods are highly sensitive to outliers and deviations from Gaussian assumptions. In such settings, nonparametric methods may be favored over parametric ones. Additionally, there is a need for statistical methods that control an overall error rate for multiple hypothesis testing. We review univariate and multivariate nonparametric hypothesis tests and apply them to longitudinal data to assess changes over time in 31 biomarkers measured from the gingival crevicular fluid in 22 subjects whereby gingivitis was induced by temporarily withholding tooth brushing. To identify biomarkers that can be induced to change, multivariate Wilcoxon signed rank tests for a set of four summary measures based upon area under the curve are applied for each biomarker and compared to their univariate counterparts. Multiple hypothesis testing methods with choice of control of the false discovery rate or strong control of the family-wise error rate are examined.

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## ‣ On the geometric modeling approach to empirical null distribution estimation for empirical Bayes modeling of multiple hypothesis testing

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Português

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48.096704%

We study the geometric modeling approach to estimating the null distribution for the empirical Bayes modeling of multiple hypothesis testing. The commonly used method is a nonparametric approach based on the Poisson regression, which however could be unduly affected by the dependence among test statistics and perform very poorly under strong dependence. In this paper, we explore a finite mixture model based geometric modeling approach to empirical null distribution estimation and multiple hypothesis testing. Through simulations and applications to two public microarray data, we will illustrate its competitive performance.

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## ‣ Spiked Dirichlet Process Prior for Bayesian Multiple Hypothesis Testing in Random Effects Models

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em //2009
Português

Relevância na Pesquisa

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We propose a Bayesian method for multiple hypothesis testing in random effects models that uses Dirichlet process (DP) priors for a nonparametric treatment of the random effects distribution. We consider a general model formulation which accommodates a variety of multiple treatment conditions. A key feature of our method is the use of a product of spiked distributions, i.e., mixtures of a point-mass and continuous distributions, as the centering distribution for the DP prior. Adopting these spiked centering priors readily accommodates sharp null hypotheses and allows for the estimation of the posterior probabilities of such hypotheses. Dirichlet process mixture models naturally borrow information across objects through model-based clustering while inference on single hypotheses averages over clustering uncertainty. We demonstrate via a simulation study that our method yields increased sensitivity in multiple hypothesis testing and produces a lower proportion of false discoveries than other competitive methods. While our modeling framework is general, here we present an application in the context of gene expression from microarray experiments. In our application, the modeling framework allows simultaneous inference on the parameters governing differential expression and inference on the clustering of genes. We use experimental data on the transcriptional response to oxidative stress in mouse heart muscle and compare the results from our procedure with existing nonparametric Bayesian methods that provide only a ranking of the genes by their evidence for differential expression.

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## ‣ Testing independent censoring for longitudinal data

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em 01/07/2011
Português

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A common problem associated with longitudinal studies is the dropouts of subjects or censoring before the end of follow-up. In most existing methods, it is assumed that censoring is noninformative about missed responses. This assumption is crucial to the validity of many statistical procedures. We develop some nonparametric hypothesis testing procedures to test for independent censoring in the absence/presence of covariates. The test statistics are constructed by contrasting two estimators of the conditional mean of cumulative responses for each stratum of covariate space from sample subsets with different patterns of censoring. Our method does not require the modelling of longitudinal response processes, therefore is robust to model misspecifications. A diagnostic plot procedure is also developed that can be used to identify dependent censoring to certain covariate strata. The finite sample performances of the tests are investigated through extensive simulation studies. The potential of our methods is demonstrated through the application of the tests to a chronic granulomatous disease study.

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## ‣ Statistical Group Comparison of Diffusion Tensors via Multivariate Hypothesis Testing

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em /06/2007
Português

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Diffusion tensor imaging (DTI) provides a powerful tool for identifying white matter (WM) alterations in clinical populations. The prevalent method for group-level analysis of DTI is statistical comparison of the diffusion tensor fractional anisotropy (FA) metric. The FA metric, however, does not capture the full orientational information contained in the diffusion tensor. For example, the FA test is incapable of detecting group-level differences in diffusion orientation when the level of anisotropy is unaffected. Here, we apply multivariate hypothesis testing procedures to the elements of the diffusion tensor as an alternative to univariate testing using FA. Both parametric and nonparametric tests are proposed with each choice carrying specific assumptions about the diffusion tensor model. Of particular interest is the Cramér test, which works on Euclidean interpoint distances and can be readily adapted to a specific non-Euclidean framework by applying matrix logarithms to the diffusion tensors. Using Monte Carlo simulations, we show that multivariate tests can detect diffusion tensor principal eigenvector differences of 15 degrees with up to 80–90% power under typical design conditions. We also show that some multivariate tests are more sensitive to FA differences...

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## ‣ Nonparametric Tests for Differential Histone Enrichment with ChIP-Seq Data

Fonte: Libertas Academica
Publicador: Libertas Academica

Tipo: Artigo de Revista Científica

Publicado em 27/01/2015
Português

Relevância na Pesquisa

47.95338%

Chromatin immunoprecipitation sequencing (ChIP-seq) is a powerful method for analyzing protein interactions with DNA. It can be applied to identify the binding sites of transcription factors (TFs) and genomic landscape of histone modification marks (HMs). Previous research has largely focused on developing peak-calling procedures to detect the binding sites for TFs. However, these procedures may fail when applied to ChIP-seq data of HMs, which have diffuse signals and multiple local peaks. In addition, it is important to identify genes with differential histone enrichment regions between two experimental conditions, such as different cellular states or different time points. Parametric methods based on Poisson/negative binomial distribution have been proposed to address this differential enrichment problem and most of these methods require biological replications. However, many ChIP-seq data usually have a few or even no replicates. We propose a nonparametric method to identify the genes with differential histone enrichment regions even without replicates. Our method is based on nonparametric hypothesis testing and kernel smoothing in order to capture the spatial differences in histone-enriched profiles. We demonstrate the method using ChIP-seq data on a comparative epigenomic profiling of adipogenesis of murine adipose stromal cells and the Encyclopedia of DNA Elements (ENCODE) ChIP-seq data. Our method identifies many genes with differential H3K27ac histone enrichment profiles at gene promoter regions between proliferating preadipocytes and mature adipocytes in murine 3T3-L1 cells. The test statistics also correlate with the gene expression changes well and are predictive to gene expression changes...

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## ‣ 18.441 Statistical Inference, Spring 2002; Statistical Inference

Fonte: MIT - Massachusetts Institute of Technology
Publicador: MIT - Massachusetts Institute of Technology

Português

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#Point and interval estimation#The maximum likelihood method#Hypothesis testing#Nonparametric methods#Chi-square goodness of fit tests#Likelihood-ratio tests and Bayesian methods#probability, statistical inference#Analysis of variance, regression analysis and correlation#Mathematical statistics#270502#Mathematical Statistics and Probability

Reviews probability and introduces statistical inference. Point and interval estimation. The maximum likelihood method. Hypothesis testing. Likelihood-ratio tests and Bayesian methods. Nonparametric methods. Analysis of variance, regression analysis and correlation. Chi-square goodness of fit tests. More theoretical than 18.443 (Statistics for Applications) and more detailed in its treatment of statistics than 18.05 (Introduction to Probability and Statistics).

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## ‣ Nonparametric Testing Methods for Treatment-Biomarker Interaction based on Local Partial-Likelihood

Fonte: Quens University
Publicador: Quens University

Tipo: Relatório

Português

Relevância na Pesquisa

58.202847%

A fair amount of research has been done on the interactions between treatment and
biomarkers hoping to avoid failure to recognize effective agents which benefit only a subset of patients in traditional clinical designs and analysis, such as (Bonetti, 2004), (Bonetti et al., 2009), and (Royston and Sauerbrei, 2004). Particularly, Fan et al. (Fan et al., 2006) assumed the treatment effect is an unknown function of a putative biomarker, and proposed techniques to give the local partial likelihood estimation (LPLE) of this treatment effect function using local linear techniques (Fan and Chen, 1999). However, no methods were developed for assessing whether the treatment
effect is indeed a function of the biomarker (interaction exists) or just a constant (no
interactions).
Based on the idea of LPLE, a new nonparametric hypothesis testing methodology,
which we call local partial likelihood bootstrap (LPLB) test, is proposed in this work to identify the differences in treatment effects among subgroups of patients with different values of biomarkers in a Phase III clinical trials study. A bootstrap technique is used to evaluate the significance of the test. Meanwhile, the proposed method can also be applied to identify the interactions between a putative biomarker and a collection of covariates (covariate vectors) that are discrete or continuous. Numerical studies show that the LPLB test can provide a substantial improvement in the power of the interaction detection compared with the commonly used method...

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## ‣ Bootstrap tests for nonparametric comparison of regression curves with dependent errors

Fonte: Springer
Publicador: Springer

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

48.202847%

In this paper, the problem of testing the equality of regression curves with dependent data is studied. Several methods based on nonparametric estimators of the regression function are described. In this setting, the distribution of the test statistic is frequently unknown or difficult to compute, so an approximate test based on the asymptotic distribution of the statistic can be considered. Nevertheless, the asymptotic properties of the methods proposed in this work have been obtained under independence of the observations, and just one of these methods was studied in a context of dependence as reported by Vilar-Fernández and González-Manteiga (Statistics 58(2):81–99, 2003). In addition, the distribution of these test statistics converges to the limit distribution with convergence rates usually rather slow, so that the approximations obtained for reasonable sample sizes are not satisfactory. For these reasons, many authors have suggested the use of bootstrap algorithms as an alternative approach. Our main concern is to compare the behavior of three bootstrap procedures that take into account the dependence assumption of the observations when they are used to approximate the distribution of the test statistics considered. A broad simulation study is carried out to observe the finite sample performance of the analyzed bootstrap tests.

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## ‣ Asymptotic equivalence and adaptive estimation for robust nonparametric regression

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/09/2009
Português

Relevância na Pesquisa

48.16648%

Asymptotic equivalence theory developed in the literature so far are only for
bounded loss functions. This limits the potential applications of the theory
because many commonly used loss functions in statistical inference are
unbounded. In this paper we develop asymptotic equivalence results for robust
nonparametric regression with unbounded loss functions. The results imply that
all the Gaussian nonparametric regression procedures can be robustified in a
unified way. A key step in our equivalence argument is to bin the data and then
take the median of each bin. The asymptotic equivalence results have
significant practical implications. To illustrate the general principles of the
equivalence argument we consider two important nonparametric inference
problems: robust estimation of the regression function and the estimation of a
quadratic functional. In both cases easily implementable procedures are
constructed and are shown to enjoy simultaneously a high degree of robustness
and adaptivity. Other problems such as construction of confidence sets and
nonparametric hypothesis testing can be handled in a similar fashion.; Comment: Published in at http://dx.doi.org/10.1214/08-AOS681 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org)

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## ‣ Hypothesis testing in the presence of multiple samples under density ratio models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

47.966025%

This paper presents a hypothesis testing method given independent samples
from a number of connected populations. The method is motivated by a forestry
project for monitoring change in the strength of lumber. Traditional practice
has been built upon nonparametric methods which ignore the fact that these
populations are connected. By pooling the information in multiple samples
through a density ratio model, the proposed empirical likelihood method leads
to a more efficient inference and therefore reduces the cost in applications.
The new test has a classical chi-square null limiting distribution. Its power
function is obtained under a class of local alternatives. The local power is
found increased even when some underlying populations are unrelated to the
hypothesis of interest. Simulation studies confirm that this test has better
power properties than potential competitors, and is robust to model
misspecification. An application example to lumber strength is included.; Comment: 38 pages, 8 figures

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## ‣ Sieve empirical likelihood ratio tests for nonparametric functions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/03/2005
Português

Relevância na Pesquisa

48.32989%

Generalized likelihood ratio statistics have been proposed in Fan, Zhang and
Zhang [Ann. Statist. 29 (2001) 153-193] as a generally applicable method for
testing nonparametric hypotheses about nonparametric functions. The likelihood
ratio statistics are constructed based on the assumption that the distributions
of stochastic errors are in a certain parametric family. We extend their work
to the case where the error distribution is completely unspecified via newly
proposed sieve empirical likelihood ratio (SELR) tests. The approach is also
applied to test conditional estimating equations on the distributions of
stochastic errors. It is shown that the proposed SELR statistics follow
asymptotically rescaled \chi^2-distributions, with the scale constants and the
degrees of freedom being independent of the nuisance parameters. This
demonstrates that the Wilks phenomenon observed in Fan, Zhang and Zhang [Ann.
Statist. 29 (2001) 153-193] continues to hold under more relaxed models and a
larger class of techniques. The asymptotic power of the proposed test is also
derived, which achieves the optimal rate for nonparametric hypothesis testing.
The proposed approach has two advantages over the generalized likelihood ratio
method: it requires one only to specify some conditional estimating equations
rather than the entire distribution of the stochastic error...

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## ‣ A Bayesian Nonparametric Hypothesis Testing Approach for Regression Discontinuity Designs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/02/2014
Português

Relevância na Pesquisa

47.95338%

The regression discontinuity (RD) design is a popular approach to causal
inference in non-randomized studies. This is because it can be used to identify
and estimate causal effects under mild conditions. Specifically, for each
subject, the RD design assigns a treatment or non-treatment, depending on
whether or not an observed value of an assignment variable exceeds a fixed and
known cutoff value.
In this paper, we propose a Bayesian nonparametric regression modeling
approach to RD designs, which exploits a local randomization feature. In this
approach, the assignment variable is treated as a covariate, and a
scalar-valued confounding variable is treated as a dependent variable (which
may be a multivariate confounder score). Then, over the model's posterior
distribution of locally-randomized subjects that cluster around the cutoff of
the assignment variable, inference for causal effects are made within this
random cluster, via two-group statistical comparisons of treatment outcomes and
non-treatment outcomes.
We illustrate the Bayesian nonparametric approach through the analysis of a
real educational data set, to investigate the causal link between basic skills
and teaching ability.

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## ‣ Two-sample Bayesian Nonparametric Hypothesis Testing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

58.566597%

In this article we describe Bayesian nonparametric procedures for two-sample
hypothesis testing. Namely, given two sets of samples
$\mathbf{y}^{\scriptscriptstyle(1)}\;$\stackrel{\scriptscriptstyle{iid}}{\s
im}$\;F^{\scriptscriptstyle(1)}$ and $\mathbf{y}^{\scriptscriptstyle(2
)}\;$\stackrel{\scriptscriptstyle{iid}}{\sim}$\;F^{\scriptscriptstyle( 2)}$,
with $F^{\scriptscriptstyle(1)},F^{\scriptscriptstyle(2)}$ unknown, we wish to
evaluate the evidence for the null hypothesis
$H_0:F^{\scriptscriptstyle(1)}\equiv F^{\scriptscriptstyle(2)}$ versus the
alternative $H_1:F^{\scriptscriptstyle(1)}\neq F^{\scriptscriptstyle(2)}$. Our
method is based upon a nonparametric P\'{o}lya tree prior centered either
subjectively or using an empirical procedure. We show that the P\'{o}lya tree
prior leads to an analytic expression for the marginal likelihood under the two
hypotheses and hence an explicit measure of the probability of the null
$\mathrm{Pr}(H_0|\{\mathbf
{y}^{\scriptscriptstyle(1)},\mathbf{y}^{\scriptscriptstyle(2)}\}\mathbf{)}$.; Comment: Published at http://dx.doi.org/10.1214/14-BA914 in the Bayesian
Analysis (http://projecteuclid.org/euclid.ba) by the International Society of
Bayesian Analysis (http://bayesian.org/)

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## ‣ On the Decreasing Power of Kernel and Distance based Nonparametric Hypothesis Tests in High Dimensions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

48.57223%

#Statistics - Machine Learning#Computer Science - Information Theory#Computer Science - Learning#Mathematics - Statistics Theory#Statistics - Methodology

This paper is about two related decision theoretic problems, nonparametric
two-sample testing and independence testing. There is a belief that two
recently proposed solutions, based on kernels and distances between pairs of
points, behave well in high-dimensional settings. We identify different sources
of misconception that give rise to the above belief. Specifically, we
differentiate the hardness of estimation of test statistics from the hardness
of testing whether these statistics are zero or not, and explicitly discuss a
notion of "fair" alternative hypotheses for these problems as dimension
increases. We then demonstrate that the power of these tests actually drops
polynomially with increasing dimension against fair alternatives. We end with
some theoretical insights and shed light on the \textit{median heuristic} for
kernel bandwidth selection. Our work advances the current understanding of the
power of modern nonparametric hypothesis tests in high dimensions.; Comment: 19 pages, 9 figures, published in AAAI-15: The 29th AAAI Conference
on Artificial Intelligence (with author order reversed from ArXiv)

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## ‣ Two-sample Bayesian nonparametric goodness-of-fit test

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

48.31913%

In recent years, Bayesian nonparametric statistics has gathered extraordinary
attention. Nonetheless, a relatively little amount of work has been expended on
Bayesian nonparametric hypothesis testing. In this paper, a novel Bayesian
nonparametric approach to the two-sample problem is established. Precisely,
given two samples $\mathbf{X}=X_1,\ldots,X_{m_1}$ $\overset {i.i.d.} \sim F$
and $\mathbf{Y}=Y_1,\ldots,Y_{m_2} \overset {i.i.d.} \sim G$, with $F$ and $G$
being unknown continuous cumulative distribution functions, we wish to test the
null hypothesis $\mathcal{H}_0:~F=G$. The method is based on the Kolmogorov
distance and approximate samples from the Dirichlet process centered at the
standard normal distribution and a concentration parameter 1. It is
demonstrated that the proposed test is robust with respect to any prior
specification of the Dirichlet process. A power comparison with several
well-known tests is incorporated. In particular, the proposed test dominates
the standard Kolmogorov-Smirnov test in all the cases examined in the paper.; Comment: 25 pages, 8 figures

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## ‣ Intentionally biased bootstrap methods

Fonte: Aiden Press
Publicador: Aiden Press

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

48.4371%

#Keywords: Bias reduction#Empirical likelihood#Hypothesis testing#Local linear smoothing#Nonparametric curve estimation#Variance stabilization#Weighted bootstrap

A class of weighted bootstrap techniques, called biased bootstrap or b-bootstrap methods, is introduced. It is motivated by the need to adjust empirical methods, such as the "uniform" bootstrap, in a surgical way to alter some of their features while leaving others unchanged. Depending on the nature of the adjustment, the b-bootstrap can be used to reduce bias, or to reduce variance or to render some characteristic equal to a predetermined quantity. Examples of the last application include a b-bootstrap approach to hypothesis testing in nonparametric contexts, where the b-bootstrap enables simulation "under the null hypothesis", even when the hypothesis is false, and a b-bootstrap competitor to Tibshirani's variance stabilization method. An example of the bias reduction application is adjustment of Nadaraya-Watson kernel estimators to make them competitive with local linear smoothing. Other applications include density estimation under constraints, outlier trimming, sensitivity analysis, skewness or kurtosis reduction and shrinkage.

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