Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Bhattacharya, Bhaskar


One of the most common tools used in statistical methodology is the regression analysis which assumes independence of data and uses the standard F-statistic to make decisions. However, for two-stage cluster samples data, the independence as- sumption fails and, consequently, the test statistic does not follow the F -distribution. It has been shown that when testing a null hypothesis with equality constraints the use of an F-distribution leads to inflated type I error for two-stage cluster samples data.When testing hypotheses with inequality constraints, the standard F-statistic is updated as the F ̄-statistic. So far the effect of two-stage cluster samples on the F ̄-statistic remained unexplored, and is the topic of this dissertation. We first in- vestigate under a normal model the effect of misspecified covariance matrix on the chibar test statistic for inequality constrained hypotheses. We proposed an adjusted chibar distribution which corrects the type I error. For the regression setup, we proposed a two-step generalized least square F ̄ test iii statistic and have shown its distribution to be of the F ̄ type. We show through simulation that the proposed test statistic performs better than the corresponding unrestricted F-test statistic in terms of type I error under the null hypothesis. It also achieves power gains under the alternative with a variety of different types of misspecification of the covariance matrix compared with the unrestricted F-test statistic.




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