Herman Chernoff was born in New York City on 1 July 1923. He went to school there and later received the B.S. degree from the City College of New York in 1943, majoring in mathematics with a minor in physics. For a year and a half, he worked as a junior physicist with the U.S. Navy, before joining Brown University for graduate work in applied mathematics. His studies were interrupted by a short period in the U.S. Army, and then his interest in statistics led him to complete his Ph.D. thesis at Columbia University under the supervision of Abraham Wald. At Brown University, Herman met Judy Ullman. They have been married since 1947 and have two daughters, Ellen and Miriam. Herman worked for the Cowles Commission at the University of Chicago and then spent three years in the Mathematics Department at the University of Illinois before joining the Department of Statistics at Stanford University in 1952, where he remained for 22 years. He moved to M.I.T. in 1974, where he founded the Statistics Center. Since 1985 he has been in the Department of Statistics at Harvard. Professor Chernoff has been honored for his contributions in many ways. He was President of the Institute of Mathematical Statistics and is an elected member of both the American Academy of Arts and Sciences and the National Academy of Sciences. The book Recent Advances in Statistics published in honor of his 60th birthday in 1983 contained papers in the fields where his influence as a researcher and teacher has been strong: design and sequential analysis...

Proceedings of the Annual Meeting of the American Statistical Association, August 5-9, 2001; We have developed a model for teaching math- ematical statistics through detailed case studies, and we have had some success with students us- ing the R and S-Plus languages to analyze data from the cases and to perform simulation studies of statistical concepts underlying the methods used in the analyses. We describe a few examples of these simulation studies, and explain how we use the computer to bridge the gap between statistical theory and practice and to develop understanding of the the basic ideas in mathematical statistics. Recently, we have embarked on a new approach that builds on the work of the Omegahat project (www.omegahat.org), which has embedded the R statistical software in the Netscape browser. We are designing interactive environments for browsers that use R for performing computations and plot- ting. The goal is to develop electronic activities that will make it easier for students to explore and develop understanding of the concepts of statistics and that will connect these concepts to the practice of statistics.

A dissertação apresenta uma abordagem prática para o ensino da matemática nos níveis fundamental e médio. De forma mais específica, apresenta conceitos de estatística básica como tratamento de informações e estudo de probabilidades. Estes conceitos são de grande importância no âmbito científico (parte experimental, por exemplo) e social (compreensão de características populacionais), além de estarem inseridos na vida cotidiana dos alunos. Sendo assim, foi entendido que é primordial desenvolver as competências e habilidades para organizar e compreender informações. Foram realizados experimentos para a aplicação dos conceitos apresentados em sala de aula. Também uma pesquisa propondo questões para analisar aspectos sobre alimentação e prática de exercícios físicos. Estes experimentos, além da aplicação dos conceitos, pretendem desenvolver no público-alvo, raciocínio lógico e olhar crítico, para assuntos relacionados à disciplina de matemática, utilizando situações cotidianas. Para análise organizamos e interpretamos as informações por meio de tabelas e gráficos. A pesquisa teve como objetivo principal mostrar como é usada a teoria estatística para a tomada de decisão e, nesse caso, para melhorar a própria qualidade de vida. Desse modo...

In this paper we present a study of the problem of approximating the expectations of functions of statistics in independent and dependent random variables in terms of the expectations of functions of the component random variables. We present results providing sharp analogues of the Burkholder--Rosenthal inequalities and related estimates for the expectations of functions of sums of dependent nonnegative r.v.'s and conditionally symmetric martingale differences with bounded conditional moments as well as for sums of multilinear forms. Among others, we obtain the following sharp inequalities: $E(\sum_{k=1}^n X_k)^t\le 2 \max (\sum_{k=1}^n EX_k^t, (\sum_{k=1}^n a_k)^t)$ for all nonnegative r.v.'s $X_1, \ldots, X_n$ with $E(X_k\mid X_1, \ldots, X_{k-1})\le a_k$, $EX_k^t<\infty$, $k=1, \ldots, n$, $1#x003C;t#x003C;2$; $E(\sum_{k=1}^n X_k)^t\le E\theta^t(1) \max (\sum_{k=1}^n b_k, (\sum_{k=1}^n a_k^s)^{t/s})$ for all nonnegative r.v.'s $X_1, \ldots, X_n$ with $E(X_k^s\mid X_1, \ldots, X_{k-1})\le a_k^s$, $E(X_k^t\mid X_1, \ldots, X_{k-1})\le b_k$, $k=1, \ldots, n$, $1#x003C;t#x003C;2$, $0#x003C;s\le t-1$ or $t\ge 2$, $0#x003C;s\le 1$, where $\theta(1)$ is a Poisson random variable with parameter 1. As applications, new decoupling inequalities for sums of multilinear forms are presented and sharp Khintchine--Marcinkiewicz--Zygmund inequalities for generalized moving averages are obtained. The results can also be used in the study of a wide class of nonlinear statistics connected to problems of long-range dependence and in an econometric setup...

I first met Leo Breiman in 1979 at the beginning of his third career, Professor of Statistics at Berkeley. He obtained his PhD with Lo\'eve at Berkeley in 1957. His first career was as a probabilist in the Mathematics Department at UCLA. After distinguished research, including the Shannon--Breiman--MacMillan Theorem and getting tenure, he decided that his real interest was in applied statistics, so he resigned his position at UCLA and set up as a consultant. Before doing so he produced two classic texts, Probability, now reprinted as a SIAM Classic in Applied Mathematics, and Statistics. Both books reflected his strong opinion that intuition and rigor must be combined. He expressed this in his probability book which he viewed as a combination of his learning the right hand of probability, rigor, from Lo\'eve, and the left-hand, intuition, from David Blackwell.; Comment: Published in at http://dx.doi.org/10.1214/10-AOAS404 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as established in machine learning. In the case where the energy distance is computed with a semimetric of negative type, a positive definite kernel, termed distance kernel, may be defined such that the MMD corresponds exactly to the energy distance. Conversely, for any positive definite kernel, we can interpret the MMD as energy distance with respect to some negative-type semimetric. This equivalence readily extends to distance covariance using kernels on the product space. We determine the class of probability distributions for which the test statistics are consistent against all alternatives. Finally, we investigate the performance of the family of distance kernels in two-sample and independence tests: we show in particular that the energy distance most commonly employed in statistics is just one member of a parametric family of kernels, and that other choices from this family can yield more powerful tests.; Comment: Published in at http://dx.doi.org/10.1214/13-AOS1140 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Moore introduced a method for graduate mathematics instruction that consisted primarily of individual student work on challenging proofs (Jones, 1977). Cohen (1982) described an adaptation with less explicit competition suitable for undergraduate students at a liberal arts college. This paper details an adaptation of this modified Moore-method to teach mathematical statistics, and describes ways that such an approach helps engage students and foster the teaching of statistics. Groups of students worked a set of 3 difficult problems (some theoretical, some applied) every two weeks. Class time was devoted to coaching sessions with the instructor, group meeting time, and class presentations. R was used to estimate solutions empirically where analytic results were intractable, as well as to provide an environment to undertake simulation studies with the aim of deepening understanding and complementing analytic solutions. Each group presented comprehensive solutions to complement oral presentations. Development of parallel techniques for empirical and analytic problem solving was an explicit goal of the course, which also attempted to communicate ways that statistics can be used to tackle interesting problems. The group problem solving component and use of technology allowed students to attempt much more challenging questions than they could otherwise solve.

An establishment's average wage, computed from administrative wage data, has been found to be related to occupational wages. These occupational wages are a primary outcome variable for the Bureau of Labor Statistics Occupational Employment Statistics survey. Motivated by the fact that nonresponse in this survey is associated with average wage even after accounting for other establishment characteristics, we propose a method that uses the administrative data for imputing missing occupational wage values due to nonresponse. This imputation is complicated by the structure of the data. Since occupational wage data is collected in the form of counts of employees in predefined wage ranges for each occupation, weighting approaches to deal with nonresponse do not adequately adjust the estimates for certain domains of estimation. To preserve the current data structure, we propose a method to impute each missing establishment's wage interval count data as an ordered multinomial random variable using a separate survival model for each occupation. Each model incorporates known auxiliary information for each establishment associated with the distribution of the occupational wage data, including geographic and industry characteristics. This flexible model allows the baseline hazard to vary by occupation while allowing predictors to adjust the probabilities of an employee's salary falling within the specified ranges. An empirical study and simulation results suggest that the method imputes missing OES wages that are associated with the average wage of the establishment in a way that more closely resembles the observed association.; Comment: Published in at http://dx.doi.org/10.1214/14-AOAS714 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We consider the detection of multivariate spatial clusters in the Bernoulli model with $N$ locations, where the design distribution has weakly dependent marginals. The locations are scanned with a rectangular window with sides parallel to the axes and with varying sizes and aspect ratios. Multivariate scan statistics pose a statistical problem due to the multiple testing over many scan windows, as well as a computational problem because statistics have to be evaluated on many windows. This paper introduces methodology that leads to both statistically optimal inference and computationally efficient algorithms. The main difference to the traditional calibration of scan statistics is the concept of grouping scan windows according to their sizes, and then applying different critical values to different groups. It is shown that this calibration of the scan statistic results in optimal inference for spatial clusters on both small scales and on large scales, as well as in the case where the cluster lives on one of the marginals. Methodology is introduced that allows for an efficient approximation of the set of all rectangles while still guaranteeing the statistical optimality results described above. It is shown that the resulting scan statistic has a computational complexity that is almost linear in $N$.; Comment: Published in at http://dx.doi.org/10.1214/09-AOS732 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

With the possible exception of gambling, meteorology, particularly precipitation forecasting, may be the area with which the general public is most familiar with probabilistic assessments of uncertainty. Despite the heavy use of stochastic models and statistical methods in weather forecasting and other areas of the atmospheric sciences, papers in these areas have traditionally been somewhat uncommon in statistics journals. We see signs of this changing in recent years and we have sought to highlight some present research directions at the interface of statistics and the atmospheric sciences in this special section.; Comment: Published in at http://dx.doi.org/10.1214/08-AOAS209 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In the first, we show that in some cases when no density exists, the integral of the formal saddlepoint density over the set corresponding to large values of the likelihood ratio-like statistic approximates the true probability with relative error of order $1/n$. In the second, we give multivariate generalizations of the Lugannani--Rice and Barndorff-Nielsen or $r^*$ formulas for the approximations. These theorems are applied to obtain permutation tests based on the likelihood ratio-like statistics for the $k$ sample and the multivariate two-sample cases. Numerical examples are given to illustrate the high degree of accuracy, and these statistics are compared to the classical statistics in both cases.; Comment: Published in at http://dx.doi.org/10.1214/11-AOS945 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

This volume is our tribute to David A. Freedman, whom we regard as one of the great statisticians of our time. He received his B.Sc. degree from McGill University and his Ph.D. from Princeton, and joined the Department of Statistics of the University of California, Berkeley, in 1962, where, apart from sabbaticals, he has been ever since. In a career of over 45 years, David has made many fine contributions to probability and statistical theory, and to the application of statistics. His early research was on Markov chains and martingales, and two topics with which he has had a lifelong fascination: exchangeability and De Finetti's theorem, and the consistency of Bayes estimates. His asymptotic theory for the bootstrap was also highly influential. David was elected to the American Academy of Arts and Sciences in 1991, and in 2003 he received the John J. Carty Award for the Advancement of Science from the U.S. National Academy of Sciences. In addition to his purely academic research, David has extensive experience as a consultant, including working for the Carnegie Commission, the City of San Francisco, and the Federal Reserve, as well as several Departments of the U.S. Government--Energy, Treasury, Justice, and Commerce. He has testified as an expert witness on statistics in a number of law cases...

Spectral sampling is associated with the group of unitary transformations acting on matrices in much the same way that simple random sampling is associated with the symmetric group acting on vectors. This parallel extends to symmetric functions, k-statistics and polykays. We construct spectral k-statistics as unbiased estimators of cumulants of trace powers of a suitable random matrix. Moreover we define normalized spectral polykays in such a way that when the sampling is from an infinite population they return products of free cumulants.; Comment: Published in at http://dx.doi.org/10.1214/13-AOS1107 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We consider the ensemble of adjacency matrices of Erd\H{o}s-R\'{e}nyi random graphs, that is, graphs on $N$ vertices where every edge is chosen independently and with probability $p\equiv p(N)$. We rescale the matrix so that its bulk eigenvalues are of order one. We prove that, as long as $pN\to\infty$ (with a speed at least logarithmic in $N$), the density of eigenvalues of the Erd\H{o}s-R\'{e}nyi ensemble is given by the Wigner semicircle law for spectral windows of length larger than $N^{-1}$ (up to logarithmic corrections). As a consequence, all eigenvectors are proved to be completely delocalized in the sense that the $\ell^{\infty}$-norms of the $\ell^2$-normalized eigenvectors are at most of order $N^{-1/2}$ with a very high probability. The estimates in this paper will be used in the companion paper [Spectral statistics of Erd\H{o}s-R\'{e}nyi graphs II: Eigenvalue spacing and the extreme eigenvalues (2011) Preprint] to prove the universality of eigenvalue distributions both in the bulk and at the spectral edges under the further restriction that $pN\gg N^{2/3}$.; Comment: Published in at http://dx.doi.org/10.1214/11-AOP734 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

The classical theory of rank-based inference is entirely based either on ordinary ranks, which do not allow for considering location (intercept) parameters, or on signed ranks, which require an assumption of symmetry. If the median, in the absence of a symmetry assumption, is considered as a location parameter, the maximal invariance property of ordinary ranks is lost to the ranks and the signs. This new maximal invariant thus suggests a new class of statistics, based on ordinary ranks and signs. An asymptotic representation theory \`{a} la H\'{a}jek is developed here for such statistics, both in the nonserial and in the serial case. The corresponding asymptotic normality results clearly show how the signs add a separate contribution to the asymptotic variance, hence, potentially, to asymptotic efficiency. As shown by Hallin and Werker [Bernoulli 9 (2003) 137--165], conditioning in an appropriate way on the maximal invariant potentially even leads to semiparametrically efficient inference. Applications to semiparametric inference in regression and time series models with median restrictions are treated in detail in an upcoming companion paper.; Comment: Published at http://dx.doi.org/10.1214/009053605000000769 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

This paper concerns the emergence of modern mathematical statistics in France after the First World War. Emile Borel's achievements are presented, and especially his creation of two institutions where mathematical statistics was developed: the {\it Statistical Institute of Paris University}, (ISUP) in 1922 and above all the {\it Henri Poincar\'e Institute} (IHP) in 1928. At the IHP, a new journal {\it Annales de l'Institut Henri Poincar\'e} was created in 1931. We discuss the first papers in that journal dealing with mathematical statistics.

The dimer model on a graph embedded in the torus can be interpreted as a collection of random self-avoiding loops. In this paper, we consider the uniform toroidal honeycomb dimer model. We prove that when the mesh of the graph tends to zero and the aspect of the torus is fixed, the winding number of the collection of loops converges in law to a two-dimensional discrete Gaussian distribution. This is known to physicists in more generality from their analysis of toroidal two-dimensional critical loop models and their mapping to the massless free field on the torus. This paper contains the first mathematical proof of this more general physics result in the specific case of the loop model induced by a toroidal dimer model.; Comment: Published in at http://dx.doi.org/10.1214/09-AOP453 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

This is the final version of the article. It first appeared from the Institute of Mathematical Statistics via http://dx.doi.org/10.1214/14-STS511; Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal process-ing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical approximations to the associated state inference problems. However, in most applications, the state-space model of interest also depends on unknown static parameters that need to be estimated from the data. In this context, standard particle methods fail and it is necessary to rely on more sophisticated algorithms. The aim of this paper is to present a comprehensive review of particle methods that have been proposed to perform static parameter estimation in state-space models. We discuss the advantages and limitations of these methods and illustrate their performance on simple models.; N. Kantas was supported by the Engineering and Physical Sciences Research Council (EPSRC) under grant EP/J01365X/1 and programme grant on Control For Energy and Sustainability (EP/G066477/1). S.S. Singh's research is partly funded by EPSRC under the First Grant Scheme (EP/G037590/1). A. Doucet's research is partly funded by EPSRC (EP/K000276/1 and EP/K009850/1). N. Chopin's research is partly by the ANR as part of the "Investissements d'Avenir" program (ANR-11-LABEX-0047).

In an election, voting power—the probability that a single vote is decisive—is affected by the rule for aggregating votes into a single outcome. Voting power is important for studying political representation, fairness and strategy, and has been much discussed in political science. Although power indexes are often considered as mathematical definitions, they ultimately depend on statistical models of voting. Mathematical calculations of voting power usually have been performed under the model that votes are decided by coin flips. This simple model has interesting implications for weighted elections, two-stage elections (such as the U.S. Electoral College) and coalition structures. We discuss empirical failings of the coin-flip model of voting and consider, first, the implications for voting power and, second, ways in which votes could be modeled more realistically. Under the random voting model, the standard deviation of the average of n votes is proportional to 1/√n, but under more general models, this variance can have the form cn^(−α) or √a−b log n. Voting power calculations undermore realistic models present research challenges in modeling and computation.

Tadeusz Caliński was born in Poznań, Poland in 1928. Despite the absence of formal secondary eduction for Poles during the Second World War, he entered the University of Poznań in 1948, initially studying agronomy and in later years mathematics. From 1953 to 1988 he taught statistics, biometry and experimental design at the Agricultural University of Poznań. During this period he founded and developed the Poznań inter-university school of mathematical statistics and biometry, which has become one of the most important schools of this type in Poland and beyond. He has supervised 24 Ph.D. students, many of whom are currently professors at a variety of universities. He is now Professor Emeritus. Among many awards, in 1995 Professor Caliński received the Order of Polonia Restituta for his outstanding achievements in the fields of Education and Science. In 2012 the Polish Statistical Society awarded him The Jerzy Spława-Neyman Medal for his contribution to the development of research in statistics in Poland. Professor Caliński in addition has Doctoral Degrees honoris causa from the Agricultural University of Poznań and the Warsaw University of Life Sciences. His research interests include mathematical statistics and biometry...