Maximum Approximate Bernstein Likelihood Estimation of Densities in a Two-sample Semiparametric Model

TL;DR

This paper introduces a new maximum approximate Bernstein likelihood method for estimating densities in a two-sample semiparametric model, demonstrating superior performance over existing methods through simulations and real data applications.

Contribution

It develops a novel Bernstein polynomial-based approach for density estimation in semiparametric models, with an EM algorithm for efficient computation.

Findings

Proposed method outperforms existing density estimation techniques in simulations.

The approach provides consistent and asymptotically normal estimators.

Real data examples illustrate practical applicability and effectiveness.

Abstract

Maximum likelihood estimators are proposed for the parameters and the densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used to obtain the maximum approximate Bernstein likelihood estimates. Simulation study shows that the performance of the proposed method is much better than the existing ones. The proposed method is illustrated by real data examples. Some asymptotic results are also presented and proved.