Adjustments of Rao’s Score Test for Distributional and Local Parametric Misspecifications

Anil K. Bera, Yannis Bilias, Mann J. Yoon, Süleyman Taşpınar*, Osman Doğan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Rao’s (1948) seminal paper introduced a fundamental principle of testing based on the score function and the score test has local optimal properties. When the assumed model is misspecified, it is well known that Rao’s score (RS) test loses its optimality. A model could be misspecified in a variety of ways. In this paper, we consider two kinds: distributional and parametric. In the former case, the assumed probability density function differs from the data generating process. Kent (1982) and White (1982) analyzed this case and suggested a modified version of the RS test that involves adjustment of the variance. In the latter case, the dimension of the parameter space of the assumed model does not match with that of the true one. Using the distribution of the RS test under this situation, Bera and Yoon (1993) developed a modified RS test that is valid under the local parametric misspecification. This involves adjusting both the mean and variance of the standard RS test. This paper considers the joint presence of the distributional and parametric misspecifications and develops a modified RS test that is valid under both types of misspecification. Earlier modified tests under either type of misspecification can be obtained as the special cases of the proposed test. We provide three examples to illustrate the usefulness of the suggested test procedure. In a Monte Carlo study, we demonstrate that the modified test statistics have good finite sample properties.

Original languageEnglish
Article number20170022
JournalJournal of Econometric Methods
Issue number1
Publication statusPublished - 1 Jan 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 Walter de Gruyter GmbH, Berlin/Boston.


  • Lagrange multiplier tests
  • QMLE
  • Rao’s score tests
  • inference
  • locally misspecified models
  • robust LM tests
  • specification testing


Dive into the research topics of 'Adjustments of Rao’s Score Test for Distributional and Local Parametric Misspecifications'. Together they form a unique fingerprint.

Cite this