A Score Test for Individual Heteroscedasticity in a One-way Error Components Model

The purpose of this paper is to derive a Rao's efficient score statistic for testing for heteroscedasticity in an error components model with only individual effects. We assume that the individual effect exists and therefore do not test for it. In addition, we assume that the individual effects, and not the white noise term may be heteroscedastic. Finally, we assume that the error components are normally distributed. We first establish, under a specific set of assumptions, the asymptotic distribution of the Score under contiguous alternatives. We then derive the expression for the Score test statistic for individual heteroscedasticity. Finally, we discuss the asymptotic local power of this Score test statistic.