Score tests for homogeneity of variances in longitudinal time series data via wavelets

Mahalingam, Nalini (2007) Score tests for homogeneity of variances in longitudinal time series data via wavelets. Masters thesis, Memorial University of Newfoundland.

[English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (1MB)

Abstract

We discuss Neyman's partial score test for homogeneity of variances in nonparametric models. We considered two data structures. First, we consider longitudinal data where the observations from each subject are generated from a nonparametric model with heteroscedastic errors. In this context, we found that the discrete wavelet transform approach used by Cai, Hurvich and Tsai (1998) does not lead to a consistent estimate of the mean response function which in turn affects the score statistic. Second, we consider longitudinal data where the observed response from each subject is assumed to be a time series that is nonstationary in mean and variance. The trend component of each series is estimated by a wavelet version of weighted least squares and the residuals are used in estimating the local variances. These estimates are used in a simulation study of the score statistic we construct for testing homoscedasticity in the longitudinal set-up. In the simulation study we examine the size and power of the test.

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