Empirical Likelihood
Series: Monographs on Statistics and Applied Probability, 92
Publisher: Chapman & Hall/CRC
Published: 2001
Place of publication: Boca Raton, FL, USA
Language: eng
Format: Hardcover
Number of pages: 320
ISBN-13: 9781584880714
Copyright date: 2001
Subjects: Applied mathematics; Probability & statistics; Probabilities; Mathematics; Science/Mathematics; Probability & Statistics - General; Mathematics / Statistics; Estimation theory; Mathematical Statistics
First sentence: Empirical likelihood is a nonparametric method of statistical inference.
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.
--back cover
Table of contents: title: Preface xiii; title: 1 Introduction 1; title: 1.1 Earthworm segments, skewness and kurtosis 2; title: 1.2 Empirical likelihood, parametric likelihood, and the bootstrap 4; title: 1.3 Bibliographic notes 6; title: 2 Empirical likelihood 7; title: 2.1 Nonparametric maximum likelihood 7; title: 2.2 Nonparametric likelihood ratios 10; title: 2.3 Ties in the data 11; title: 2.4 Multinomial on the sample 12; title: 2.5 EL for a univariate mean 16; title: 2.6 Coverage accuracy 17; title: 2.7 One-sided coverage levels 19; title: 2.8 Power and efficiency 20; title: 2.9 Computing EL for a univariate mean 21; title: 2.10 Empirical discovery of parametric families 24; title: 2.11 Bibliographic notes 25; title: 2.12 Exercises 27; title: 3 EL for random vectors 29; title: 3.1 NPMLE for IID vectors 29; title: 3.2 EL for a multivariate mean 30; title: 3.3 Fisher, Bartlett, and bootstrap calibration 31; title: 3.4 Smooth functions of means 35; title: 3.5 Estimating equations 39; title: 3.6 EL for quantiles 43; title: 3.7 Ties and quantiles 45; title: 3.8 Likelihood-based estimating equations 48; title: 3.9 Transformation invariance of EL 50; title: 3.10 Side information 51; title: 3.11 Sandwich estimator 55; title: 3.12 Robust estimators 56; title: x CONTENTS; title: 3.13 Robust likelihood 59; title: 3.14 Computation and convex duality 60; title: 3.15 Euclidean likelihood 63; title: 3.16 Other nonparametric likelihoods 66; title: 3.17 Bibliographic notes 70; title: 3.18 Exercises 74; title: 4 Regression and modeling 79; title: 4.1 Random predictors 79; title: 4.2 Nonrandom predictors 83; title: 4.3 Triangular array ELT 85; title: 4.4 Analysis of variance 87; title: 4.5 Variance modeling 90; title: 4.6 Nonlinear least squares 91; title: 4.7 Generalized linear models 95; title: 4.8 Poisson regression 101; title: 4.9 Calibration, prediction, and tolerance regions 104; title: 4.10 Euclidean likelihood for regression and ANOVA 106; title: 4.11 Bibliographic notes 107; title: 4.12 Exercises 108; title: 5 Empirical likelihood and smoothing 111; title: 5.1 Kernel estimates 111; title: 5.2 Bias and variance 113; title: 5.3 EL for kernel smooths 114; title: 5.4 Blood pressure trajectories 116; title: 5.5 Conditional quantiles 117; title: 5.6 Simultaneous inference 118; title: 5.7 An additive model 121; title: 5.8 Bibliographic notes 124; title: 5.9 Exercises 125; title: 6 Biased and incomplete samples 127; title: 6.1 Biased sampling 127; title: 6.2 Multiple biased samples 130; title: 6.3 Truncation and censoring 135; title: 6.4 NPMLE’s for censored and truncated data 139; title: 6.5 Product-limit estimators 141; title: 6.6 EL for right censoring 143; title: 6.7 Proportional hazards 147; title: 6.8 Further empirical likelihood ratio results 147; title: 6.9 Bibliographic notes 149; title: 6.10 Exercises 153; title: CONTENTS xi; title: 7 Bands for distributions 155; title: 7.1 The ECDF 156; title: 7.2 Exact calibration of ECDF bands 157; title: 7.3 Asymptotics of bands 158; title: 7.4 Bibliographic notes 160; title: 8 Dependent data 163; title: 8.1 Time series 163; title: 8.2 Reducing to independence 165; title: 8.3 Blockwise empirical likelihood 168; title: 8.4 Spectral method 173; title: 8.5 Finite populations 174; title: 8.6 MELE’s using side information 176; title: 8.7 Sampling designs 177; title: 8.8 Empirical likelihood ratios for finite populations 179; title: 8.9 Other dependent data 180; title: 8.10 Bibliographic notes 180; title: 8.11 Exercises 183; title: 9 Hybrids and connections 185; title: 9.1 Product of parametric and empirical likelihoods 185; title: 9.2 Parametric conditional likelihood 186; title: 9.3 Parametric models for data ranges 187; title: 9.4 Empirical likelihood and Bayes 188; title: 9.5 Bayesian bootstrap 188; title: 9.6 Least favorable families and nonparametric tilting 189; title: 9.7 Bootstrap likelihood 191; title: 9.8 Bootstrapping from an NPMLE 191; title: 9.9 Jackknives 192; title: 9.10 Sieves 194; title: 9.11 Bibliographic notes 196; title: 9.12 Exercises 199; title: 10 Challenges for EL 201; title: 10.1 Symmetry 201; title: 10.2 Independence 207; title: 10.3 Comparison to permutation tests 208; title: 10.4 Convex hull condition 209; title: 10.5 Inequality and qualitative constraints 210; title: 10.6 Nonsmooth estimating equations 211; title: 10.7 Adverse estimating equations and black boxes 213; title: 10.8 Bibliographic notes 213; title: 10.9 Exercises 215; title: xii CONTENTS; title: 11 Some proofs 217; title: 11.1 Lemmas 217; title: 11.2 Univariate and Vector ELT 219; title: 11.3 Triangular array ELT 222; title: 11.4 Multi-sample ELT 223; title: 11.5 Bibliographic notes 226; title: 12 Algorithms 229; title: 12.1 Statistical tasks 230; title: 12.2 Smooth optimization 232; title: 12.3 Estimating equation methods 234; title: 12.4 Partial derivatives 238; title: 12.5 Primal problem 241; title: 12.6 Sequential linearization 244; title: 12.7 Bibliographic notes 247; title: 13 Higher order asymptotics 249; title: 13.1 Bartlett correction 249; title: 13.2 Bartlett correction and smooth functions of means 250; title: 13.3 Pseudo-likelihood theory 251; title: 13.4 Signed root corrections 253; title: 13.5 Large deviations 255; title: 13.6 Bibliographic notes 257; title: 13.7 Exercises 258; title: Appendix 261; title: A.1 Order and stochastic order notation 261; title: A.2 Parametric models 262; title: A.3 Likelihood 264; title: A.4 The bootstrap idea 266; title: A.5 Bootstrap confidence intervals 267; title: A.6 Better bootstrap confidence intervals 269; title: A.7 Bibliographic notes 271; title: References 273; title: Author index 287; title: Subject index 293