Asymptotic Variance of Test Statistics in the ML and QML Frameworks

Anil K. Bera, Osman Doğan, Süleyman Taşpınar

Research output: Contribution to journalArticlepeer-review


In this study, we consider the test statistics that can be written as the sample average of data and derive their limiting distributions under the maximum likelihood (ML) and the quasi-maximum likelihood (QML) frameworks. We first generalize the asymptotic variance formula suggested in Pierce (Ann Stat 10(2):475–478, 1982) in the ML framework and illustrate its applications through some well-known test statistics: (1) the skewness statistic, (2) the kurtosis statistic, (3) the Cox statistic, (4) the information matrix test statistic, and (5) 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.

Original languageEnglish (US)
Article number2
JournalJournal of Statistical Theory and Practice
Issue number1
StatePublished - Mar 1 2021


  • Asymptotic variance
  • Durbin’s h-statistic
  • Inference
  • Kurtosis statistic
  • MLE
  • QMLE
  • Skewness statistic
  • Test statistics
  • The Cox statistic
  • The information matrix test
  • Variance

ASJC Scopus subject areas

  • Statistics and Probability


Dive into the research topics of 'Asymptotic Variance of Test Statistics in the ML and QML Frameworks'. Together they form a unique fingerprint.

Cite this