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Heteroscedasticity Testing in Nonparametric Functional Data Statistics

Mustapha Rachdi, Halima Bensmail, Noriah Al-Kandari, Idir Ouassou

Abstract



We present a consistent nonparametric test statistic for heteroscedasticity in functional data. First we construct the test by evaluating the difference between conditional and unconditional variances. Then we show the asymptotic normality of this test statistic under null hypothesis. In addition, we prove that this test is also consistent against all deviations from the homoscedasticity condition.

Keywords


Functional data analysis (FDA), Nonparametric test, Nonparametric functional data analysis (NFDA), Kernel estimate, U-statistic.

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