Empirical Likelihood: 1st Edition (Hardback) book cover

Empirical Likelihood

1st Edition

By Art B. Owen

Chapman and Hall/CRC

304 pages | 40 B/W Illus.

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Hardback: 9781584880714
pub: 2001-05-18
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Description

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 also facilitates incorporating side information, and it simplifies accounting for censored, truncated, or biased sampling.

One of the first books published on the subject, Empirical Likelihood offers an in-depth treatment of this method for constructing confidence regions and testing hypotheses. The author applies empirical likelihood to a range of problems, from those as simple as setting a confidence region for a univariate mean under IID sampling, to problems defined through smooth functions of means, regression models, generalized linear models, estimating equations, or kernel smooths, and to sampling with non-identically distributed data. Abundant figures offer visual reinforcement of the concepts and techniques. Examples from a variety of disciplines and detailed descriptions of algorithms-also posted on a companion Web site at-illustrate the methods in practice. Exercises help readers to understand and apply the methods.

The method of empirical likelihood is now attracting serious attention from researchers in econometrics and biostatistics, as well as from statisticians. This book is your opportunity to explore its foundations, its advantages, and its application to a myriad of practical problems.

Reviews

"In this beautifully written book Owen lucidly illustrates the wide applicability of empirical likelihood and provides masterful accounts of its latest theoretical developments. Numerous empirical examples should fascinate practitioners in various fields of science. I recommend this book extremely highly."

-Yuichi Kitamura, Department of Economics, University of Pennsylvania

"The statistical model discovery and information recovery process is shrouded in a great deal of uncertainty. Owen's empirical likelihood procedure provides an attractive basis for how best to represent the sampling process and to carry through the estimation and inference objectives"

- George Judge, University of California, Berkeley

"A great amount of thought and care has gone into preparing this fascinating monograph. Empirical likelihood is somehow at the junction between two of the main streams of contemporary statistics, parametric and nonparametric methods. Through EL, some of the key results of the former (such as Wilks' Theorem and Bartlett correctibility) carry over to the latter in a way which seems almost to deny the infinite-parameter character of nonparametric statistics. Even if the purpose of empirical likelihood was no more than this didactic one, it would be significant. Yet as Owen shows so engagingly, EL also has a colourful life of its own. It is a unique practical tool, and it enjoys important, and growing, connections to many areas of statistics, from the Kaplan-Meier estimator to the bootstrap and beyond. If we look at statistics from the vantage point of EL we can see a long way; Owen shows us how, and how far."

-Professor Peter Hall, Australian National University.

"This impressive monograph is the definitive source for researchers who wish to learn how to utilize empirical likelihood methods. The author addresses a range of topics, including univariate confidence intervals, regression models, kernel smoothing, and mean function smoothing. Although the book covers considerable ground and is rigorous, the book is well written and a reader with a solid background in mathematical statistics can readily tackle this volume."

-Journal of Mathematical Psychology

This book will make accessible to a wider audience the new and important area of nonparameteric likelihood and hypothesis testing. Masterfully written by a pioneer in this area, this book lucidly discusses the statistical theory and -- perhaps more importantly for applied econometricians -- computational details and practical aspects of putting the ideas to work with real data. This book will have a major impact on the way hypothesis testing is done in econometrics, where one is very often unsure about what the correct model specification is.

-Anand V. Bodapati, UCLA Anderson School of Management, USA

"The book will make an ideal text for a course in empirical likelihood for advanced statistics students, while it provides theoretically-minded practitioners a quick access to the growing empirical likelihood literature… The writing style is extremely clear throughout, even when discussing the fine points of the theory. Important results are well motivated, discussed and illustrated by real data examples."

-Biometrics, vol. 57, no. 4, December 2001

Table of Contents

EMPIRICAL LIKELIHOOD (EL)

Introduction

Empirical Distribution Function

Nonparametric Maximum Likelihood

Nonparametric Likelihood Ratios

Ties in the Data

Multinomial on the Sample

EL for a Univariate Mean

Coverage Accuracy

Power and Efficiency

Empirical versus Parametric Inferences

Computing the Empirical Likelihood

EL FOR RANDOM VECTORS

NPMLE for Random Vectors

EL for a Multivariate Mean

Fisher, Bartlett, and Bootstrap Calibration

Smooth Functions of Means

Estimating Equations

Transformation Invariance of EL

Using Side Information

Convex dual Problem

Unconstrained Dual Problem

Solving the Dual Problem

Euclidean Likelihood

Other Nonparametric Likelihoods

REGRESSION AND MODELING

Sampling Pairs

Fixed Regressors

Triangular Array ELT

Analysis of Variance

Variance Modeling

Nonlinear Least Squared

Generalized Linear Models

Generalized Projection Pursuit

Plastic pipe Data

Euclidean likelihood for Regression and ANOVA

SYMMETRY AND INDEPENDENCE

Testing Symmetry

Constraining to Symmetry

Approximate Symmetry

Symmetric Unimodal Distributions

Testing Independence

Constraining to Independence

Approximate Independence

Permutation Tests

IMPERFECTLY OBSERVED DATA

Biased Sampling

Truncation

Multiple Biased Samples

Censoring

CURVE ESTIMATION

Kernel Estimates

Bias and Variance

EL for Kernel Smooths

Blood Pressure Trajectories

Simultaneous Inference

Bands for the ECDF

Bands for the Quantile Function

DEPENDENT DATA

Reducing to Independence

Blockwise Empirical Likelihood

Hierarchical Data

Dual likelihood for Martingales

HYBRIDS AND CONNECTIONS

Parametric Models for Subsets of Data

Parametric Models for Components of the Data

Parametric Models for Data Ranges

Empirical Likelihood and Bayes

Bayesian Bootstrap

Nonparametric tilting Bootstrap

Weighted Likelihood Bootstrap

Bootstrap Likelihoods

Jackknifes

SOME PROOFS

Lemmas

Vector ELT

Triangular Array ELT

Multisample ELT

ALGORITHMS

Smooth Optimization

Simple Hypotheses

Composite Hypotheses

Overdetermined NPMLE

Constraints

Partial Derivatives

Nested Algorithms

Gradient Equations

Primal Problem

Sequential Linearization

Sequential Linearization and Estimating Equations

Semi-infinite Programming

Profiling Empirical Likelihoods

HIGHER ORDER ASYMPTOTICS

Bartlett Correction

Pseudo-Likelihood Theory

Signed Root Corrections

Least Favorable Families

Large Deviations

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General