多元函数型数据均值函数的假设检验

Hypothesis test for the mean function in multivariate functional data

均值函数的检验是多元函数型数据中统计建模及理论研究的重要问题.针对这个问题,本文提出了两种检验方法,并且从理论上证明了两个检验统计量在原假设下依分布渐近收敛到加权卡方分布.同时得到了借助多元函数主成分方法降维后的检验统计量的渐近分布.根据是否标准化,统计量分别收敛到卡方分布和加权卡方分布.最后通过数值模拟以及将提出的检验统计量应用到步法数据和加拿大天气数据上,可以看出两种新的检验方法都有良好的检验功效.

The test of the mean function is an important problem in the statistical modeling and the theoretical research of multivariate functional data.This paper proposes two novel test methods for this problem.We show that under the null hypothesis,the two statistics asymptotically converge to a weighted chi-square distribution.Moreover,they are also asymptotically convergent after dimension 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.