Finite Sample Correction for Two-Sample Inference with Sparse Covariate Adjusted Functional Data
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This work is motivated by the problem of testing for differences in the mean electricity prices before and after Germany's abrupt nuclear phaseout after the nuclear disaster in Fukushima Daiichi, Japan, in mid-March 2011. Given the nature of the data, we approach this problem using a Local Linear Kernel (LLK) estimator for the nonparametric mean function of sparse covariate adjusted functional data. We demonstrate that the two-sample test statistic based on existing asymptotic results suffers from severe size-distortions. Motivated by this finding, we propose a theory-based finite sample correction for the considered LLK estimator. Our simulation study shows that this finite sample correction is very effective in eliminating the size-distortions. The practical use of the procedure is demonstrated in our real data application, where we address some open questions on the differences in the mean electricity prices before and after Germany's (partial) nuclear phaseout.
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