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Abstract:
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The assumption of constant variance or homoscedasticity is often used for fitting a model to the given data. Violation of this assumption may lead an inefficient model or wrong standard error estimation. Particularly for functional data, it is difficult to validate such assumptions using simple tools like graphical devices. In this work we propose a simple test to validate this assumption. Our approach is based on a minimum distance measure of heteroscedasticity, which is zero in the case where variance is constant and positive otherwise. We derive an explicit form of the measure, propose an estimator for the quantity and investigate asymptotic properties of the proposed estimator. We use the established asymptotic distribution to construct a test for the hypothesis of homoscedasticity. We show the validity of our method for post-hoc test for fitting simple linear regression and ARMA model to functional data. We investigate the performance our method using numerical simulation and data example.
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