Parameterization and Two-Stage Conditional Maximum Likelihood Estimation

Abstract

This paper considers the case where, after appropriate reparameterization, the probability density function can be factorized into a marginal density function and a conditional density function such that one of them involves fewer parameters. Then, two types of two-stage conditional maximum-likelihood estimators, 2SCMLEI and 2SCMLEII, can be considered according to whether the marginal or the conditional density has fewer parameters. Our first result indicates that, under some identification assumptions, there is a connection between the number of parameters in the marginal (or conditional) density functions under the two reparameterizations. Moreover, conditions for asymptotic equivalence and numerical equivalence between these two-stage estimators and the FIML estimator are obtained. Finally, examples are provided to illustrate our results.

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