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Empirical Likelihood

By: Art B Owen

CRC Press

Hardback | May 2001 | #192541 | ISBN: 1584880716
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NHBS Price: £85.99 $112/€97 approx

About this book

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.

This book 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.


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

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