What question did this study set out to answer?

The research aims to derive and compare the asymptotic properties of preliminary test maximum likelihood estimators and their unrestricted counterparts.

September 1, 1979Open Access

Asymptotic Properties of Maximum Likelihood Estimators Based on Conditional Specification

Key Points

The research aims to derive and compare the asymptotic properties of preliminary test maximum likelihood estimators and their unrestricted counterparts.
Derived asymptotic distribution, bias, and dispersion matrix for preliminary test maximum likelihood estimator.
Compared these properties with unrestricted and restricted maximum likelihood estimators.
Analyzed performance under scenarios where null hypothesis constraints may not hold.
Established asymptotic properties indicating robustness of preliminary test maximum likelihood estimator.
Showed comparison values of bias and dispersion between estimator types.
Highlighted that robustness holds even when assumptions about parameters are violated.

Abstract

Along with the asymptotic distribution, expressions for the asymptotic bias and asymptotic dispersion matrix of the preliminary test maximum likelihood estimator for a general multi-sample parametric model (when the null hypothesis relating to the restraints on the parameters may not hold) are derived and compared with the parallel expressions for the unrestricted and restricted maximum likelihood estimators. This study reveals the robustness property of the preliminary test estimator when the assumed restraints may not hold.

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