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Introduction to Empirical Processes and Semiparametric Inference de Michael R. Kosorok

Introduction to Empirical Processes and Semiparametric Inference

Autor Michael R. Kosorok
en Limba Engleză Hardback – 31 ian 2008

Observăm că utilitatea practică a volumului Introduction to Empirical Processes and Semiparametric Inference rezidă în capacitatea sa de a oferi instrumente riguroase pentru analizarea modelelor statistice complex-realiste, depășind limitările modelelor parametrice clasice. Michael R. Kosorok propune o abordare didactică a unor tehnici de cercetare adesea considerate opace, oferind o punte de legătură necesară către literatura de specialitate de nivel înalt. Subliniem faptul că, deși tratează subiecte avansate, textul este structurat ca un manual, facilitând tranziția cercetătorilor către utilizarea proceselor empirice în inferența semiparametrică.

Din punct de vedere al ariei tematice, lucrarea acoperă segmente similare cu Mathematical Statistics de Peter J. Bickel, însă se diferențiază printr-o focalizare mult mai specifică pe procesele empirice și o introducere mai graduală, dar la fel de riguroasă, în complexitatea spațiului parametrilor. Spre deosebire de Asymptotic Statistics de A. W. van der Vaart, care oferă o privire de ansamblu asupra aproximărilor prin experimente limită, volumul de față prioritizează aplicabilitatea metodelor de tip M-estimatori și Z-estimatori în contextul inferenței pe eșantioane mari.

Structura cărții este remarcabil de echilibrată, alternând teoria pură cu „Case Studies”. Primele capitole pun bazele convergenței stocastice și ale metodelor de entropie, progresând natural către bootstrapping și rezultate funcționale complexe. Reținem organizarea în trei blocuri majore: fundamentarea proceselor empirice, urmată de mecanismele inferenței semiparametrice (atât pentru parametri fini, cât și infiniți), totul fiind ancorat în exemple practice care validează conceptele matematice expuse.

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Specificații

ISBN-13: 9780387749778
ISBN-10: 0387749772
Pagini: 500
Ilustrații: XIV, 483 p.
Dimensiuni: 160 x 241 x 32 mm
Greutate: 0.91 kg
Ediția:2008
Editura: Springer
Locul publicării:New York, NY, United States

Public țintă

Research

De ce să citești această carte

Recomandăm această lucrare statisticienilor și cercetătorilor care doresc să stăpânească tehnici moderne de inferență fără a se pierde în abstractizarea extremă a monografiilor de nișă. Cititorul câștigă o înțelegere clară a modului în care procesele empirice pot fi aplicate în estimarea modelelor complexe. Este resursa ideală pentru cei care se pregătesc pentru un doctorat în statistică sau econometrie, oferind un parcurs de învățare structurat și studii de caz aplicate.

Descriere scurtă

The goal of this book is to introduce statisticians, and other researchers with a background in mathematical statistics, to empirical processes and semiparametric inference. These powerful research techniques are surpr- ingly useful for studying large sample properties of statistical estimates from realistically complex models as well as for developing new and - proved approaches to statistical inference. This book is more of a textbook than a research monograph, although a number of new results are presented. The level of the book is more - troductory than the seminal work of van der Vaart and Wellner (1996). In fact, another purpose of this work is to help readers prepare for the mathematically advanced van der Vaart and Wellner text, as well as for the semiparametric inference work of Bickel, Klaassen, Ritov and We- ner (1997). These two books, along with Pollard (1990) and Chapters 19 and 25 of van der Vaart (1998), formulate a very complete and successful elucidation of modern empirical process methods. The present book owes much by the way of inspiration, concept, and notation to these previous works.What is perhaps new is the gradual—yetrigorous—anduni?ed way this book introduces the reader to the ?eld.

Cuprins

Overview.- An Overview of Empirical Processes.- Overview of Semiparametric Inference.- Case Studies I.- Empirical Processes.- to Empirical Processes.- Preliminaries for Empirical Processes.- Stochastic Convergence.- Empirical Process Methods.- Entropy Calculations.- Bootstrapping Empirical Processes.- Additional Empirical Process Results.- The Functional Delta Method.- Z-Estimators.- M-Estimators.- Case Studies II.- Semiparametric Inference.- to Semiparametric Inference.- Preliminaries for Semiparametric Inference.- Semiparametric Models and Efficiency.- Efficient Inference for Finite-Dimensional Parameters.- Efficient Inference for Infinite-Dimensional Parameters.- Semiparametric M-Estimation.- Case Studies III.

Recenzii

From the reviews:
"Introduction to Empirical Processes and Semiparametric Inference is a very good combination of both the empirical processes and semiparametric theories. This is the first book of its kind....I agree with the author that this book is 'more of a textbook than a research monograph.' As the semiparametric inference is currently an extremely active research area in statistical research, the book will open the door for graduate students to identify significant future research potentials. In fact, this book contains the author's newest research result, the application of semiparametric method in microarray data analysis. This book can be used as a textbook for graduate students in statistics, biostatistics, and economics (econometrics). In fact, the contents of this book can be tailored for different courses."
"Generally, this is a great book on empirical processes and semiparametric methods. It should be on the must-read list for a serious statistician, biostatistician, or econometrician." (Biometrics, September 2008)
"The main focus of this book is to introduce empirical processes and semiparametric inference methods to researchers interested in developing inferential tools for relatively complicated mathematical or statistical modeling problems. ...The material is structured in a sensible way supporting the learning and understanding of useful and challenging techniques of empirical processes and semiparametric inference. The book could well be very helpful for those studying and applying these techniques." (International Statistical Review 2008,77,2)
“This book is an introduction to what is commonly called the modern theory of empirical processes – empirical processes indexed by classes of functions – and to semiparametric inference, and the interplay between both fields. … This is clearly intended to be a book for the novice in empirical process theory and semiparametricinference. … The main material is presented in a clearly arranged and logical order. … will be useful to anybody who wants to learn about the modern theory of empirical processes and semiparametric inference.” (Erich Häusler, Zentralblatt MATH, Vol. 1180, 2010)

Textul de pe ultima copertă

This book provides a self-contained, linear, and unified 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. The targeted audience includes statisticians, biostatisticians, and other researchers with a background in mathematical statistics who have an interest in learning about and doing research in empirical processes and semiparametric inference but who would like to have a friendly and gradual introduction to the area. The book can be used either as a research reference or as a textbook. The level of the book is suitable for a second year graduate course in statistics or biostatistics, provided the students have had a year of graduate level mathematical statistics and a semester of probability.
The book consists of three parts. The first part is a concise overview of all of the main concepts covered in the book with a minimum of technicalities. The second and third parts cover the two respective main topics of empirical processes and semiparametric inference in depth. The connections between these two topics is also demonstrated and emphasized throughout the text. Each part has a final chapter with several case studies that use concrete examples to illustrate the concepts developed so far. The last two parts also each include a chapter which covers the needed mathematical preliminaries. Each main idea is introduced with a non-technical motivation, and examples are given throughout to illustrate important concepts. Homework problems are also included at the end of each chapter to help the reader gain additional insights.
Michael R. Kosorok is Professor and Chair, Department of Biostatistics, and Professor, Department of Statistics and Operations Research, at the University of North Carolina at Chapel Hill. His research has focused on the application of empirical processes and semiparametric inference to statistics and biostatistics. He is a Fellow of both the American Statistical Association and the Institute of Mathematical Statistics. He is an Associate Editor of the Annals of Statistics, Electronic Journal of Statistics, International Journal of Biostatistics, Statistics and Probability Letters, and Statistics Surveys.