A pair of novel priors for improving and extending the conditional MLE

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 asymptotically 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.

Automated summary

A Bayesian estimator is proposed to improve the conditional maximum likelihood estimation by introducing a pair of priors. The conditional maximum likelihood estimation is explained using the posterior mode under a prior, and a promising estimator is defined using the posterior mean under a corresponding prior. The advantages of this 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.