Reparametrization of the least favorable submodel in semi-parametric multisample models

TL;DR

This paper investigates the efficiency of estimators in semi-parametric multisample models using reparametrization of the least favorable submodel, aiming to reduce computational complexity and establish conditions for efficiency.

Contribution

It provides conditions under which the efficient score and information can be expressed in reparametrized models, enhancing understanding of estimator efficiency.

Findings

Derived conditions for efficient score representation

Established links between reparametrization and estimator efficiency

Improved computational approaches for semi-parametric models

Abstract

The method of estimation in Scott and Wild (Biometrika 84 (1997) 57--71 and J. Statist. Plann. Inference 96 (2001) 3--27) uses a reparametrization of the profile likelihood that often reduces the computation times dramatically. Showing the efficiency of estimators for this method has been a challenging problem. In this paper, we try to solve the problem by investigating conditions under which the efficient score function and the efficient information matrix can be expressed in terms of the parameters in the reparametrized model.