Parameterization and Two-Stage Conditional Maximum Likelihood Estimation

1985/07/01 by Da‐Hsiang Donald Lien, Lien, Da-Hsiang Donald, Quang Vuong +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Distribution Estimation and Applications #Statistical Methods and Inference

paper · doi:10.7907/ccwfw-y7228

openalex publication_date 1985/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Related

• Conditional Density Estimation by Penalized Likelihood Model Selection and Applications
• Conditional Density Estimation via Weighted Logistic Regressions
• MLE's bias pathology, Model Updated Maximum Likelihood Estimates and Wallace's Minimum Message Length method
• On Asymptotic Analysis of the Two-Stage Approach: Towards Data-Driven Parameter Estimation
• The Constrained Maximum Likelihood Estimation For Parameters Arising From Partially Identified Models