Hybrid combinations of parametric and empirical likelihoods.

ABSTRACT: This paper develops a hybrid likelihood (HL) method based on a compromise between parametric and nonparametric likelihoods. Consider the setting of a parametric model for the distribution of an observation Y with parameter ?. Suppose there is also an estimating function m(·, ?) identifying another parameter ? via Em(Y, ?) = 0, at the outset defined independently of the parametric model. To borrow strength from the parametric model while obtaining a degree of robustness from the empirical likelihood method, we formulate inference about ? in terms of the hybrid likelihood function Hn (?) = Ln (?)1-a Rn (?(?)) a . Here a ? [0,1) represents the extent of the compromise, Ln is the ordinary parametric likelihood for ?, Rn is the empirical likelihood function, and ? is considered through the lens of the parametric model. We establish asymptotic normality of the corresponding HL estimator and a version of the Wilks theorem. We also examine extensions of these results under misspecification of the parametric model, and propose methods for selecting the balance parameter a.

SUBMITTER: Hjort NL 

PROVIDER: S-EPMC6602551 | biostudies-literature | 2018 Oct

REPOSITORIES: biostudies-literature