Empirical likelihood (Q2756704)

This book deals with the empirical likelihood (EL) which is a nonparametric method of inference based on a datadriven likelihood ratio function, and emphasizes analyzing data in ways that illustrate the power and flexibility of EL inference. In very little detail, first the LR inference is discussed through a nonparametric likelihood ratio function. In Chapters 3 and 4, the EL is discussed for smooth functions of means, and for estimating equations which provide an extremely flexible way to describe parameters and the corresponding statistics, and there are also given EL inferences for linear regression and other models with covariates, such as generalized linear models. Chapters 5 and 6 give an adaption of the EL to curve estimation problems such as density estimation and nonparametric regression, and consider EL inference in some nonstandard sampling settings such as biased sampling.NEWLINENEWLINENEWLINEIn Chapters 7 and 8, the author considers confidence bands for distribution functions and some related functions, and discusses EL for the dependent data like a time series. Chapters 9 through 11 consider hybrid methods in which EL is combined with other methods, and discuss problems where EL has difficulties and ways of mitigating these difficulties, and also contain some of the proofs of the EL theorems. In Chapters 12 and 13, the author describes how to approach the optimization problems posed by EL, and emphasizes to compute the EL for statistics defined through estimating equations, with nuisance parameters and side constraints, and also discusses some theory of higher order asymptotics.