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Activity Number: 309
Type: Contributed
Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Learning and Data Mining
Abstract #314794
Title: Multi-Sample Equal-Covariance Function Testing
Author(s): Jia Guo* and Jin-Ting Zhang
Companies: National University of Singapore and National University of Singapore
Keywords: $L^2$-norm based test ; Welch-Satterthwaite $\chi^2$-approximation ; functional data ; multi-sample problem ; covariance function
Abstract:

We propose an $L^2$-norm based test for the multi-sample equal covariance function (ECF) testing problem. The test statistic is obtained via globalizing the difference between the estimated individual and common covariance functions and it is asymptotically a $\chi^2$-type mixture. Using the Welch-Satterthwaite $\chi^2$-approximation, the null is approximately a scaled $\chi^2$ distribution. We use the naive method and bias-reduced method for estimating the scale parameter and the degrees of freedom of the above distribution. We also propose a random permutation method to directly approximate the critical values of the $L^2$-norm based test statistic. The asymptotic power is investigated and the $L^2$-norm based method is shown to be root-n consistent. Simulation studies find that in terms of size-controlling and power, the $L^2$-norm based tests outperform the two-sample test proposed in Fremdt et al. (2012) when the functional data are less correlated. Applications to the orthosis data (Abramovich et al. (2004)) and the egg-laying curves of fruit flies (M{\"u}ller and Stadtm{\"u}ller (2005)) are presented.


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