  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.
