Asymptotic Variance of Test Statistics in ML and QML Frameworks
Posted: 27 Nov 2017 Last revised: 25 Sep 2020
Date Written: February 8, 2019
Abstract
In this study, we consider the test statistics that can be written as the sample average of data and derive their limiting distribution under the maximum likelihood (ML) and the quasi-maximum likelihood (QML) frameworks. We first generalize the asymptotic variance formula suggested in Pierce (1982) in the ML framework and illustrate its applications through some well-known test statistics: (i) the skewness statistic, (ii) the kurtosis statistic, (iii) the Cox statistic, (iv) the information matrix test statistic, and (v) the Durbin's h-statistic. We next provide a similar result in the QML setting and illustrate its applications by providing two examples. Illustrations show the simplicity and the effectiveness of our results for the asymptotic variance of test statistics, and therefore, they are recommended for practical applications.
Keywords: Variance, Asymptotic variance, MLE, QMLE, Inference, Test statistics, Skewness statistic, Kurtosis statistic, The Cox's statistic, The information matrix test, the Durbin's h-statistic
JEL Classification: C13, C21, C31
Suggested Citation: Suggested Citation