A Pair of Novel Priors for Improving and Extending the Conditional MLE

TL;DR

This paper introduces a pair of novel Bayesian priors that enhance the conditional maximum likelihood estimator by leveraging posterior mean estimators with advantageous optimality properties and flexible extensions.

Contribution

It proposes a new pair of priors for Bayesian estimation that improve upon the conditional MLE and facilitate extensions and finite sample treatments.

Findings

The proposed priors lead to estimators with optimality properties.

The approach simplifies extensions and finite sample analysis.

The method is compared favorably to existing approaches.

Abstract

A Bayesian estimator aiming at improving the conditional MLE is proposed by introducing a pair of priors. After explaining the conditional MLE by the posterior mode under a prior, we define a promising estimator by the posterior mean under a corresponding prior. The prior is equivalent to the reference prior in familiar models. Advantages of the present approach include two different optimality properties of the induced estimator, the ease of various extensions and the possible treatments for a finite sample size. The existing approaches are discussed and critiqued.