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Empirical Likelihood

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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


"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 impressivemonograph 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

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