This paper generalizes the methodology of Cat and Brown [Cai, T., Brown, L.D., 1998. Wavelet shrinkage for nonequispaced samples. The Annals of Statistics 26, 1783-1799] for wavelet shrinkage for nonequispaced samples, but in the presence of correlated stationary Gaussian errors. If the true function is a member of a piecewise Holder class, it is shown that, even for long memory errors, the rate of convergence of the procedure is almost-minimax relative to the independent and identically distributed errors case. (c) 2008 Elsevier B.V. All rights reserved.; CNPq; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); FAPESP[03/10105-2]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

In this paper, we propose nonlinear elliptical models for correlated data with heteroscedastic and/or autoregressive structures. Our aim is to extend the models proposed by Russo et al. [22] by considering a more sophisticated scale structure to deal with variations in data dispersion and/or a possible autocorrelation among measurements taken throughout the same experimental unit. Moreover, to avoid the possible influence of outlying observations or to take into account the non-normal symmetric tails of the data, we assume elliptical contours for the joint distribution of random effects and errors, which allows us to attribute different weights to the observations. We propose an iterative algorithm to obtain the maximum-likelihood estimates for the parameters and derive the local influence curvatures for some specific perturbation schemes. The motivation for this work comes from a pharmacokinetic indomethacin data set, which was analysed previously by Bocheng and Xuping [1] under normality.; FAPESP; FAPESP; FACEPE; FACEPE; CNPq (Brazil); CNPq, Brazil

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...

Employment and earnings statistics are the key link between the size and structure of economic growth and the welfare of households, which is the ultimate goal of development policy, so it is important to monitor employment outcomes consistently. A cursory review of employment data for low-income Sub-Saharan African countries shows both large gaps and improbable variation within countries over time and among countries, suggesting that low quality data are routinely reported by national statistics offices. Unfortunately, policies are formed and projects developed and implemented on the basis of these statistics. Therefore, errors of measurement could be having profound implications on the strategic priorities and policies of a country. This paper explains the improbable results observed by using data from Uganda, where the labor module contains variation both within and across surveys, to show the sensitivity of employment outcomes to survey methodology. It finds that estimates of employment outcomes are unreliable if the questionnaire did not use screening questions...

Compositional data consist of known compositions vectors whose components are positive and defined in the interval (0,1) representing proportions or fractions of a "whole". The sum of these components must be equal to one. Compositional data is present in different knowledge areas, as in geology, economy, medicine among many others. In this paper, we introduce a Bayesian analysis for compositional regression applying additive log-ratio (ALR) transformation and assuming uncorrelated and correlated errors. The Bayesian inference procedure based on Markov Chain Monte Carlo Methods (MCMC). The methodology is illustrated on an artificial and a real data set of volleyball.

We present a nonparametric method for estimating the value and several derivatives of an unknown, sufficiently smooth real-valued function of real-valued arguments from a finite sample of points, where both the function arguments and the corresponding values are known only up to measurement errors having some assumed distribution and correlation structure. The method, Moving Taylor Bayesian Regression (MOTABAR), uses Bayesian updating to find the posterior mean of the coefficients of a Taylor polynomial of the function at a moving position of interest. When measurement errors are neglected, MOTABAR becomes a multivariate interpolation method. It contains several well-known regression and interpolation methods as special or limit cases. We demonstrate the performance of MOTABAR using the reconstruction of the Lorenz attractor from noisy observations as an example.; Comment: 22 pages, 4 figures

We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In the present paper a new approach is introduced to determine efficient designs for nonlinear least squares estimation which addresses the problem of correlation between observations corresponding to the same subject. We use asymptotic arguments to derive optimal design densities, and the designs for finite sample sizes are constructed from the quantiles of the corresponding optimal distribution function. It is demonstrated that compared to the optimal exact designs, whose determination is a hard numerical problem, these designs are very efficient. Alternatively, the designs derived from asymptotic theory could be used as starting designs for the numerical computation of exact optimal designs. Several examples of linear and nonlinear models are presented in order to illustrate the methodology. In particular, it is demonstrated that naively chosen equally spaced designs may lead to less accurate estimation.; Comment: Published in at http://dx.doi.org/10.1214/09-AOAS324 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We investigate the ability of current implementations of galaxy group finders to recover colour-dependent halo occupation statistics. To test the fidelity of group catalogue inferred statistics, we run three different group finders used in the literature over a mock that includes galaxy colours in a realistic manner. Overall, the resulting mock group catalogues are remarkably similar, and most colour-dependent statistics are recovered with reasonable accuracy. However, it is also clear that certain systematic errors arise as a consequence of correlated errors in group membership determination, central/satellite designation, and halo mass assignment. We introduce a new statistic, the halo transition probability (HTP), which captures the combined impact of all these errors. As a rule of thumb, errors tend to equalize the properties of distinct galaxy populations (i.e. red vs. blue galaxies or centrals vs. satellites), and to result in inferred occupation statistics that are more accurate for red galaxies than for blue galaxies. A statistic that is particularly poorly recovered from the group catalogues is the red fraction of central galaxies as function of halo mass. Group finders do a good job in recovering galactic conformity, but also have a tendency to introduce weak conformity when none is present. We conclude that proper inference of colour-dependent statistics from group catalogues is best achieved using forward modelling (i.e....

When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted explicitly. These are important pieces of information since statistical errors scale differently and often more favorably with the sample size than most systematical or theoretical errors. In this communication we describe a transparent procedure by which the statistical and systematic error components of the combination uncertainty can be obtained. We develop a general method and derive a general formula for the case of Gaussian errors with or without correlations. The method can easily be applied to other error distributions, as well. For the case of two measurements, we also define disparity and misalignment angles, and discuss their relation to the combination weight factors.; Comment: 11 pages

Many scientific and economic problems involve the analysis of high-dimensional time series datasets. However, theoretical studies in high-dimensional statistics to date rely primarily on the assumption of independent and identically distributed (i.i.d.) samples. In this work, we focus on stable Gaussian processes and investigate the theoretical properties of $\ell _1$-regularized estimates in two important statistical problems in the context of high-dimensional time series: (a) stochastic regression with serially correlated errors and (b) transition matrix estimation in vector autoregressive (VAR) models. We derive nonasymptotic upper bounds on the estimation errors of the regularized estimates and establish that consistent estimation under high-dimensional scaling is possible via $\ell_1$-regularization for a large class of stable processes under sparsity constraints. A key technical contribution of the work is to introduce a measure of stability for stationary processes using their spectral properties that provides insight into the effect of dependence on the accuracy of the regularized estimates. With this proposed stability measure, we establish some useful deviation bounds for dependent data, which can be used to study several important regularized estimates in a time series setting.; Comment: Published at http://dx.doi.org/10.1214/15-AOS1315 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

In recursive linear models, the multivariate normal joint distribution of all variables exhibits a dependence structure induced by a recursive (or acyclic) system of linear structural equations. These linear models have a long tradition and appear in seemingly unrelated regressions, structural equation modelling, and approaches to causal inference. They are also related to Gaussian graphical models via a classical representation known as a path diagram. Despite the models' long history, a number of problems remain open. In this paper, we address the problem of computing maximum likelihood estimates in the subclass of `bow-free' recursive linear models. The term `bow-free' refers to the condition that the errors for variables $i$ and $j$ be uncorrelated if variable $i$ occurs in the structural equation for variable $j$. We introduce a new algorithm, termed Residual Iterative Conditional Fitting (RICF), that can be implemented using only least squares computations. In contrast to existing algorithms, RICF has clear convergence properties and finds parameter estimates in closed form whenever possible.; Comment: 22 pages; removed an incorrect identifiability claim

We propose a class of difference-based estimators for the autocovariance in nonparametric regression when the signal is discontinuous (change-point model), possibly highly fluctuating, and the errors form a stationary $m$-dependent Gaussian process. These estimators circumvent the explicit pre-estimation of the unknown regression function, a task that is particularly challenging in change-point regression with correlated errors. We provide finite sample expressions for their mean squared errors when the signal function is piecewise constant. Based on this, we distinguish the signal as the major source of the mean squared errors and derive biased-optimized estimates. These optimal estimates do not depend on the particular (unknown) autocovariance structure, and notably, for positive correlated errors, in addition, they minimize that part of the variance which is influenced by the unknown regression function. Further, we provide some asymptotic analysis of our estimators. We show their $\sqrt{n}$-consistency in the context of a piecewise H\"older signal with non-Gaussian stationary $m$-dependent errors and when the number of change-points tends to infinity. Finally, we combine our biased-optimized autocovariance estimates with a projection-based approach and derive covariance matrix estimates for change-point regression...

A general structural equation model is fitted on a panel data set that consists of $I$ correlated samples. The correlated samples could be data from correlated populations or correlated observations from occasions of panel data. We consider cases in which the full pseudo-normal likelihood cannot be used, for example, in highly unbalanced data where the participating individuals do not appear in consecutive years. The model is estimated by a partial likelihood that would be the full and correct likelihood for independent and normal samples. It is proved that the asymptotic standard errors (a.s.e.'s) for the most important parameters and an overall-fit measure are the same as the corresponding ones derived under the standard assumptions of normality and independence for all the observations. These results are very important since they allow us to apply classical statistical methods for inference, which use only first- and second-order moments, to correlated and nonnormal data. Via a simulation study we show that the a.s.e.'s based on the first two moments have negligible bias and provide less variability than the a.s.e.'s computed by an alternative robust estimator that utilizes up to fourth moments. Our methodology and results are applied to real panel data...

Mediation analysis assesses the effect passing through a intermediate variable (mediator) in a causal pathway from the treatment variable to the outcome variable. Structure equation model (SEM) is a popular approach to estimate the mediation effect. However, causal interpretation usually requires strong assumptions, such as ignorability of the mediator, which may not hold in many social and scientific studies. In this paper, we use mediation analysis in an fMRI experiment to assess the effect of randomized binary stimuli passing through a brain pathway of two brain regions. We propose a two-layer SEM framework for mediation analysis that provides valid inference even if correlated additive errors are present. In the first layer, we use a liner SEM to model the subject level fMRI data, where the continuous mediator and outcome variables may contain correlated additive errors. We propose a constrained optimization approach to estimate the model coefficients, analyze its asymptotic properties, and characterize the nonidentifiability issue due to the correlation parameter. To address the identifiability issue, we introduce a linear mixed effects SEM with an innovation to estimate the unknown correlation parameter in the first layer, instead of sensitivity analysis. Using extensive simulated data and a real fMRI dataset...

We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has a power spectral density varying as $1/f^\gamma$. We present an accurate and fast [O(N)] algorithm for parameter estimation based on computing the likelihood in a wavelet basis. The method is illustrated and tested using simulated time-series photometry of exoplanetary transits, with particular attention to estimating the midtransit time. We compare our method to two other methods that have been used in the literature, the time-averaging method and the residual-permutation method. For noise processes that obey our assumptions, the algorithm presented here gives more accurate results for midtransit times and truer estimates of their uncertainties.; Comment: Accepted in ApJ. Illustrative code may be found at http://www.mit.edu/~carterja/code/ . 17 pages

In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is provided, which extends the classical equivalence theory for optimal designs in models with uncorrelated errors to the case of dependent data. If the regression functions are eigenfunctions of an integral operator defined by the covariance kernel, it is shown that the corresponding measure defines a universally optimal design. For several models universally optimal designs can be identified explicitly. In particular, it is proved that the uniform distribution is universally optimal for a class of trigonometric regression models with a broad class of covariance kernels and that the arcsine distribution is universally optimal for the polynomial regression model with correlation structure defined by the logarithmic potential. To the best knowledge of the authors these findings provide the first explicit results on optimal designs for regression models with correlated observations, which are not restricted to the location scale model.; Comment: Published in at http://dx.doi.org/10.1214/12-AOS1079 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We construct a "hyperparameter matrix" statistical method for performing the joint analyses of multiple correlated astronomical data sets, in which the weights of data sets are determined by their own statistical properties. This method is a generalization of the hyperparameter method constructed by Lahav et al. (2000) and Hobson, Bridle, & Lahav (2002) which was designed to combine independent data sets. The advantage of our method is to treat correlations between multiple data sets and gives appropriate relevant weights of multiple data sets with mutual correlations. We define a new "element-wise" product, which greatly simplifies the likelihood function with hyperparameter matrix. We rigorously prove the simplified formula of the joint likelihood and show that it recovers the original hyperparameter method in the limit of no covariance between data sets. We then illustrate the method by applying it to a demonstrative toy model of fitting a straight line to two sets of data. We show that the hyperparameter matrix method can detect unaccounted systematic errors or underestimated errors in the data sets. Additionally, the ratio of Bayes' factors provides a distinct indicator of the necessity of including hyperparameters. Our example shows that the likelihood we construct for joint analyses of correlated data sets can be widely applied to many astrophysical systems.; Comment: 13 pages...

We report experimental observations of correlated-photon statistics in the single-photon detection rate. The usual quantum interference in a two-photon polarization interferometer always accompanies a dip in the single detector counting rate, regardless of whether a dip or peak is seen in the coincidence rate. This effect is explained by taking into account all possible photon number states that reach the detector, rather than considering just the state post-selected by the coincidence measurement. We also report an interferometeric scheme in which the interference peak or dip in coincidence corresponds directly to a peak or dip in the single-photon detection rate.; Comment: 4 pages, two-column (minor errors corrected.)

The Guide to the Expression of Uncertainty in Measurement advocates the use of an 'effective number of degrees of freedom' for the calculation of an interval of measurement uncertainty. However, it does not describe how this number is to be calculated when (i) the measurand is a vector quantity or (ii) when the errors in the estimates of the quantities defining the measurand (the 'input quantities') are not incurred independently. An appropriate analysis for a vector-valued measurand has been described (Metrologia 39 (2002) 361-9), and a method for a one-dimensional measurand with dependent errors has also been given (Metrologia 44 (2007) 340-9). This paper builds on those analyses to present a method for the situation where the problem is multidimensional and involves correlated errors. The result is an explicit general procedure that reduces to simpler procedures where appropriate. The example studied is from the field of radio-frequency metrology, where measured quantities are often complex-valued and can be regarded as vectors of two elements.; Comment: 30 pages with 2 embedded figures

Background: Previous data reports inpatient antiretroviral (ARV) and opportunistic infection (OI) medication errors in as many as 86% of patients, with averages ranging from 1.16-2.7 errors/patient. Objective: To determine the occurrence and type of inpatient ARV and OI medication errors at our institution. Methods: A retrospective, observational, electronic medical chart review of patients with HIV/AIDS admitted between February 15, 2011- May 22, 2012 was conducted to assess the occurrence and type of ARV and OI medication errors. Secondary outcomes included assessing each medication with an error and evaluating its potential for a medication error, calculating a medication error rate per patient, evaluating whether a non-formulary (NF) medication impacted the error potential, determining whether a clinical pharmacist on service decreased the medication error rate, and assessing whether patients who experienced an error were more likely to have a longer length of stay (LOS). Analysis included descriptive statistics, averages, and Spearmen rank correlation. Results: There were 344 patients included in this analysis, 132 (38%) experienced 190 medication errors (1.44 errors/patient). An omitted order was the most frequent ARV error and accounted for 30% (n=57) of total errors. There were 166 patients requiring OI medications...