Two-sample testing for mean functions with incompletely observed functional data
type: Item
instance of: scholarly article
title: Two-sample testing for mean functions with incompletely observed functional data
zbMATH Open document ID: 1437.62706
author: Yan-Qiu Zhou
author: Yan-ling Wan
author: Tao Zhang
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2020-04-15T00:00:00Z
review text: 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.
reviewed by: Pavel Stoynov
Mathematics Subject Classification ID: 62R10
Mathematics Subject Classification ID: 62P12
zbMATH DE Number: 7189530
zbMATH Keywords: functional data analysis
zbMATH Keywords: significance test
zbMATH Keywords: incompletely observed functional data
zbMATH Keywords: mean function
MaRDI profile type: Publication
full work available at URL: s10255-020-0934-3
OpenAlex ID: W3015794290
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DOI: 10.1007/S10255-020-0934-3
description: scientific article; zbMATH DE number 7189530