324 Pages 40 B/W Illustrations
    by Chapman & Hall

    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.

    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
    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
    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
    Testing Symmetry
    Constraining to Symmetry
    Approximate Symmetry
    Symmetric Unimodal Distributions
    Testing Independence
    Constraining to Independence
    Approximate Independence
    Permutation Tests
    Biased Sampling
    Multiple Biased Samples
    Kernel Estimates
    Bias and Variance
    EL for Kernel Smooths
    Blood Pressure Trajectories
    Simultaneous Inference
    Bands for the ECDF
    Bands for the Quantile Function
    Reducing to Independence
    Blockwise Empirical Likelihood
    Hierarchical Data
    Dual likelihood for Martingales
    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
    Vector ELT
    Triangular Array ELT
    Multisample ELT
    Smooth Optimization
    Simple Hypotheses
    Composite Hypotheses
    Overdetermined NPMLE
    Partial Derivatives
    Nested Algorithms
    Gradient Equations
    Primal Problem
    Sequential Linearization
    Sequential Linearization and Estimating Equations
    Semi-infinite Programming
    Profiling Empirical Likelihoods
    Bartlett Correction
    Pseudo-Likelihood Theory
    Signed Root Corrections
    Least Favorable Families
    Large Deviations


    Owen, Art B.

    "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