STUDENTIZED PARTIAL SCORE TESTS FOR VARIANCES IN LONGITUDINAL DATA

Koenker⁹ studied a studentized version of Neyman's score statistic and obtained theoretical results which indicated that the studentized version will outperform the score test under a linear model if the data is from a heavy-tailed t-distribution. However, the author failed to examine the size and power performances of the studentized test through a simulation study. Subsequently, Cai, Hurvich and Tsai⁷ after a simulation study in a nonparametric setting, found that even when the data is from a normal population the score test was biased in estimating a pre-assigned level of significance. Thus, he recommended that the studentized score test should be used in all situations. Several authors have, however, shown earlier that when the data is from a normal population, Neyman's partial score test is asymptotically unbiased in estimating a pre-assigned level of significance. As a result in this paper, we obtain the partial score statistic and the studentized version under various models but conduct our simulation studies under the special case considered by Cai et al.⁷ in order to examine the studentized test. We found, in our simulation studies, that when the model of interest is nonparametric with uncorrelated errors, the power of the score test is generally higher than that of the studentized test. The difference in power performances becomes more pronounced under the heavy-tailed t-distribution. In the normal case, both the partial score test and its studentized version performed well in controlling the size of the test. We also found that if the score statistic is constructed based on the underlying distribution of the data, then the score statistic will always outperform the studentized test in both power and size.