多样本函数型数据的均值检验

Mean Test for Multiple-sample Functional Data

比较多样本函数型数据的均值差异一般使用高次多项式合数据,进而进行均值检验。然而一些数据结构复杂,使用高次多项式拟合效果波动较大,拟合效果欠佳,检验结果也不准确。鉴于此,文章提出使用非参数回归方法拟合数据,进而对多样本函数型数据进行均值比较检验。首先提出了两类函数型数据,通过对数据集进行光滑处理或建立适合的回归方程,得到在任意状态下的样品预测值函数,然后将固定状态下的拟合数据作为截面数据,从而可对其进行方差分析及t检验,并通过数据模拟,验证该方法的可行性。

In order to compare the mean difference of multiple-sample functional data, the higher order polynomial fitting data is generally used to combine the data, and then to conduct mean test. However, some data structures are complex, and the fitting effect of using higher-order polynomials fluctuates greatly, with poor fitting effect. Besides, the test results are not accurate. In view of this, the paper proposes a non-parametric regression method to fit the data, and then carries out the mean comparison test for multiple-sample functional data. Firstly, two types of functional data are put forward, and the data set is smoothed or a proper regression equation is established to obtain the predicted value function of the sample in any state. Secondly, the fitting data in a fixed state are taken as cross-sectional data so as to conduct ANOVA and t-test on it. Finally, the feasibility of the proposed method is verified by data simulation.