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This book contains the lecture notes for a DMV course presented by the authors at Gunzburg, Germany, in September, 1990. In the course we sketched the theory of information bounds for non parametric and semiparametric models, and developed the theory of non parametric maximum likelihood estimation in several particular inverse problems: interval censoring and deconvolution models. Part I, based on Jon Wellner's lectures, gives a brief sketch of information lower bound theory: Hajek's convolution theorem and extensions, useful minimax bounds for parametric problems due to Ibragimov and Has'minskii, and a recent result characterizing differentiable functionals due to van der Vaart (1991). The differentiability theorem is illustrated with the examples of interval censoring and deconvolution (which are pursued from the estimation perspective in part II). The differentiability theorem gives a way of clearly distinguishing situations in which 1 2 the parameter of interest can be estimated at rate n / and situations in which this is not the case. However it says nothing about which rates to expect when the functional is not differentiable. Even the casual reader will notice that several models are introduced, but not pursued in any detail; many problems remain. Part II, based on Piet Groeneboom's lectures, focuses on non parametric maximum likelihood estimates (NPMLE's) for certain inverse problems. The first chapter deals with the interval censoring problem.
This book contains the lecture notes for a DMV course presented by the authors at Gunzburg, Germany, in September, 1990. In the course we sketched the theory of information bounds for non parametric and semiparametric models, and developed the theory of non parametric maximum likelihood estimation in several particular inverse problems: interval censoring and deconvolution models. Part I, based on Jon Wellner's lectures, gives a brief sketch of information lower bound theory: Hajek's convolution theorem and extensions, useful minimax bounds for parametric problems due to Ibragimov and Has'minskii, and a recent result characterizing differentiable functionals due to van der Vaart (1991). The differentiability theorem is illustrated with the examples of interval censoring and deconvolution (which are pursued from the estimation perspective in part II). The differentiability theorem gives a way of clearly distinguishing situations in which 1 2 the parameter of interest can be estimated at rate n / and situations in which this is not the case. However it says nothing about which rates to expect when the functional is not differentiable. Even the casual reader will notice that several models are introduced, but not pursued in any detail; many problems remain. Part II, based on Piet Groeneboom's lectures, focuses on non parametric maximum likelihood estimates (NPMLE's) for certain inverse problems. The first chapter deals with the interval censoring problem.
This book collects and unifies statistical models and methods that have been proposed for analyzing interval-censored failure time data. It provides the first comprehensive coverage of the topic of interval-censored data and complements the books on right-censored data. The focus of the book is on nonparametric and semiparametric inferences, but it also describes parametric and imputation approaches. This book provides an up-to-date reference for people who are conducting research on the analysis of interval-censored failure time data as well as for those who need to analyze interval-censored data to answer substantive questions.
The thirteen papers in "Structural Analysis of Discrete Data" are previously unpublished major research contributions solicited by the editors. They have been specifically prepared to fulfill the two-fold purpose of the volume, first to provide the econometrics student with an overview of the present extent of the subject and to delineate the boundaries of current research, both in terms of methodology and applications. "Coordinated publication of important findings" should, as the editors state, "lower the cost of entry into the field and speed dissemination of recent research into the graduate econometrics classroom."A second purpose of the volume is to communicate results largely reported in the econometrics literature to a wider community of researchers to whom they are directly relevant, including applied econometricians, statisticians in the area of discrete multivariate analysis, specialists in biometrics, psychometrics, and sociometrics, and analysts in various applied fields such as finance, marketing, and transportation.The papers are grouped into four sections: "Statistical Analysis of Discrete Probability Models, " with papers by the editors and by Steven Cosslett; "Dynamic Discrete Probability Models, " consisting of two contributions by James Heckman; "Structural Discrete Probability Models Derived from Theories of Choice, " with papers by Daniel McFadden, Gregory Fischer and Daniel Nagin, Steven Lerman and Charles Manski, and Moshe Ben-Akiva and Thawat Watanatada; and "Simultaneous Systems Models with Discrete Endogenous Variables, " with contributions by Lung-Fei Lee, Jerry Hausman and David Wise, Dale Poirier, Peter Schmidt, and Robert Avery.Among the applications treated are income maintenance experiments, physician behavior, consumer credit, and intra-urban location and transportation.
A thorough and definitive book that fully addresses traditional and modern-day topics of nonparametric statistics This book presents a practical approach to nonparametric statistical analysis and provides comprehensive coverage of both established and newly developed methods. With the use of MATLAB, the authors present information on theorems and rank tests in an applied fashion, with an emphasis on modern methods in regression and curve fitting, bootstrap confidence intervals, splines, wavelets, empirical likelihood, and goodness-of-fit testing. Nonparametric Statistics with Applications to Science and Engineering begins with succinct coverage of basic results for order statistics, methods of categorical data analysis, nonparametric regression, and curve fitting methods. The authors then focus on nonparametric procedures that are becoming more relevant to engineering researchers and practitioners. The important fundamental materials needed to effectively learn and apply the discussed methods are also provided throughout the book. Complete with exercise sets, chapter reviews, and a related Web site that features downloadable MATLAB applications, this book is an essential textbook for graduate courses in engineering and the physical sciences and also serves as a valuable reference for researchers who seek a more comprehensive understanding of modern nonparametric statistical methods.
About three years ago, an idea was discussed among some colleagues in the Division of Statistics at the University of California, Davis, as to the possibility of holding an international conference, focusing exclusively on nonparametric curve estimation. The fruition of this idea came about with the enthusiastic support of this project by Luc Devroye of McGill University, Canada, and Peter Robinson of the London School of Economics, UK. The response of colleagues, contacted to ascertain interest in participation in such a conference, was gratifying and made the effort involved worthwhile. Devroye and Robinson, together with this editor and George Metakides of the University of Patras, Greece and of the European Economic Communities, Brussels, formed the International Organizing Committee for a two week long Advanced Study Institute (ASI) sponsored by the Scientific Affairs Division of the North Atlantic Treaty Organization (NATO). The ASI was held on the Greek Island of Spetses between July 29 and August 10, 1990. Nonparametric functional estimation is a central topic in statistics, with applications in numerous substantive fields in mathematics, natural and social sciences, engineering and medicine. While there has been interest in nonparametric functional estimation for many years, this has grown of late, owing to increasing availability of large data sets and the ability to process them by means of improved computing facilities, along with the ability to display the results by means of sophisticated graphical procedures.
Empirical likelihood provides inferences whose validity does not depend on specifying a parametric model for the data. Because it uses a likelihood, the method has certain inherent advantages over resampling methods: it uses the data to determine the shape of the confidence regions, and it makes it easy to combined data from multiple sources. It al
In 1984, the University of Bonn (FRG) and the International Institute for Applied System Analysis (IIASA) in Laxenburg (Austria), created a joint research group to analyze the relationship between economic growth and structural change. The research team was to examine the commodity composition as well as the size and direction of commodity and credit flows among countries and regions. Krelle (1988) reports on the results of this "Bonn-IIASA" research project. At the same time, an informal IIASA Working Group was initiated to deal with prob lems of the statistical analysis of economic data in the context of structural change: What tools do we have to identify nonconstancy of model parameters? What type of models are particularly applicable to nonconstant structure? How is forecasting affected by the presence of nonconstant structure? What problems should be anticipated in applying these tools and models? Some 50 experts, mainly statisticians or econometricians from about 15 countries, came together in Lodz, Poland (May 1985); Berlin, GDR (June 1986); and Sulejov, Poland (September 1986) to present and discuss their findings. This volume contains a selected set of those conference contributions as well as several specially invited chapters.
Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow students to understand the theoretical underpinnings of statistical methodology. The author concentrates on inferential procedures within the framework of parametric models, but - acknowledging that models are often incorrectly specified - he also views estimation from a non-parametric perspective. Overall, Mathematical Statistics places greater emphasis on frequentist methodology than on Bayesian, but claims no particular superiority for that approach. It does emphasize, however, the utility of statistical and mathematical software packages, and includes several sections addressing computational issues. The result reaches beyond "nice" mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry.