Two-sample testing for mean functions with incompletely observed functional data
The authors consider two independent samples \(Y_i(t_j)=\mu(t_j)+\epsilon_i(t_j)\), \(i=1,\dots,n\), \(j=1,\dots,N\), and \(Y^{\star}_k(t_j)=\mu^{\star}(t_j)+\epsilon^{\star}_k(t_j)\), \(k=1,\dots,m\), \(j=1,\dots,N\), where \(\mu(t)\) and \(\mu^{\star}(t)\) denote the population mean function of two independent samples, \(\epsilon_i(t)\) and \(\epsilon^{\star}_k(t)\) are two corresponding error functions with \(E{\epsilon_i(t)} = 0\) and \(E{\epsilon^{\star}_k(t)} = 0.\) It is supposed that \(Y_i(t)\) or \(Y^{\star}_k(t)\) for some \(i\) or \(k\) were not fully recorded. With these settings, the authors propose a method for testing equivalence of mean functions of the two samples. Some asymptotic results of the proposed methods are established. The proposed test is employed to analyze an environmental pollution study in Liuzhou City of China. Simulations show that the proposed test has a good control of the type-I error, and is more powerful than the complete case test in most cases.
scientific article; zbMATH DE number 7189530
scientific article