Statistical inference for Functional data: two sample Behrens-Fisher problem

With modern technology development, functional data analysis (FDA) has received considerable recent attention in many scientific fields. The estimation of mean in FDA is of interest, because it is not only important by itself but it is a prelude to other issues such as dimension reduction and modeling of functional data In this paper we construct 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. The power of the proposed test is also investigated. 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.