Asymptotic Variance of Test Statistics in ML and QML Frameworks

Posted: 27 Nov 2017 Last revised: 25 Sep 2020

See all articles by Anil K. Bera

Anil K. Bera

University of Illinois at Urbana-Champaign - Department of Economics

Osman Dogan

CUNY The Graduate Center - Department of Economics

Suleyman Taspinar

CUNY Queens College, Department of Economics

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

Bera, Anil K. and Dogan, Osman and Taspinar, Suleyman, Asymptotic Variance of Test Statistics in ML and QML Frameworks (February 8, 2019). Available at SSRN: https://ssrn.com/abstract=3074778 or http://dx.doi.org/10.2139/ssrn.3074778

Anil K. Bera

University of Illinois at Urbana-Champaign - Department of Economics ( email )

410 David Kinley Hall
1407 W. Gregory
Urbana, IL 61801
United States
217-333-4596 (Phone)
217-244-6678 (Fax)

Osman Dogan

CUNY The Graduate Center - Department of Economics ( email )

365 Fifth Avenue, 5th Floor
New York, NY 10016
United States

Suleyman Taspinar (Contact Author)

CUNY Queens College, Department of Economics ( email )

Flushing, NY 11367
United States

Do you have negative results from your research you’d like to share?

Paper statistics

Abstract Views
777
PlumX Metrics