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Asymptotic Statistics
This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.
An Introduction to Mathematical Statistics
This book gives an introduction into mathematical statistics.
Empirical Processes with Applications to Statistics
Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables; applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods; and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition. Audience: researchers in statistical theory, probability theory, biostatistics, econometrics, and computer science.
Fundamentals of Nonparametric Bayesian Inference
Bayesian nonparametrics comes of age with this landmark text synthesizing theory, methodology and computation.
Mathematical Foundations of Infinite-Dimensional Statistical Models
In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.
Lectures on Probability Theory and Statistics
This volume contains lectures given at the Saint-Flour Summer School of Probability Theory during the period 8th-24th July, 1999. We thank the authors for all the hard work they accomplished. Their lectures are a work of reference in their domain. The School brought together 85 participants, 31 of whom gave a lecture concerning their research work. At the end of this volume you will find the list of participants and their papers. Finally, to facilitate research concerning previous schools we give here the number of the volume of "Lecture Notes" where they can be found: Lecture Notes in Mathematics 1975: n ° 539- 1971: n ° 307- 1973: n ° 390- 1974: n ° 480- 1979: n ° 876- 1976: n ° 598-...
Introduction to Empirical Processes and Semiparametric Inference
Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.
High Dimensional Probability II
High dimensional probability, in the sense that encompasses the topics rep resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advan...
General Topology
"The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure," noted the Bulletin of the American Mathematical Society upon the 1955 publication of John L. Kelley's General Topology. This comprehensive treatment for beginning graduate-level students immediately found a significant audience, and it remains a highly worthwhile and relevant book for students of topology and for professionals in many areas. A systematic exposition of the part of general topology that has proven useful in several branches of mathematics, this volume is especially intended as background for modern analysis. An extensive preliminary chapter presents mathematical foundations for the main text. Subsequent chapters explore topological spaces, the Moore-Smith convergence, product and quotient spaces, embedding and metrization, and compact, uniform, and function spaces. Each chapter concludes with an abundance of problems, which form integral parts of the discussion as well as reinforcements and counter examples that mark the boundaries of possible theorems. The book concludes with an extensive index that provides supplementary material on elementary set theory.
