  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. Taking into
account the nature of the data and the auction design of the electricity
market, we approach this problem using a Local Linear Kernel (LLK) estimator
for the nonparametric mean function of sparse covariate-adjusted functional
data. We build upon recent theoretical work on the LLK estimator and propose a
two-sample test statistics using a finite sample correction to avoid size
distortions. Our nonparametric test results on the price differences point to a
Simpson's paradox explaining an unexpected result recently reported in the
literature.
