Hypothesis test for mean function in multivariate functional data

Abstract

The test of mean functions is an important 问题 in the statistical modeling and the theoretical research of multivariate functional data. This paper proposes two novel test methods for this 问题. We show that under the null hypothesis,the two statistics asymptotically converge to a weighted chi-square distribution. Moreover, they are also asymptotically convergent afterdimension reduction by means of multivariate functional principal components. Depending on whether standardized or not,the statistics converge to a chi-square distribution and a weighted chi-square distribution, respectively. Finally, the performance is investigated by both simulation studies and real examples of gait data and Canadian weather data, which show that the two new test methods have good test efficacy.