A Behrens-Fisher Problem for functional data with increasing dimension and its application

In functional data analysis (FDA), inference about the mean function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA procedures. In this paper we propose a two-sample Behrens-Fisher problem when data are functions and obtain the asymptotic properties of the test statistic as data dimension increases with the sample size. We also derive the asymptotic power of the test under some local alternativesand show that the test statistic is root-n consistent. The proposed test used for inference about the differences in the mean temperature functions of the Western and the South-western weather stations of Iran.

کلیدواژه ها:

Behrens-Fisher problem ، weather stations of Iran ، root-n consistent ، Two-sample test