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Linear hypothesis testing for weighted functional data with applications
Author(s) -
Smaga Łukasz,
Zhang JinTing
Publication year - 2020
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12414
Subject(s) - mathematics , pointwise , test statistic , functional data analysis , estimator , statistical hypothesis testing , statistics , functional principal component analysis , infimum and supremum , covariance , null distribution , null hypothesis , statistic , econometrics , discrete mathematics , mathematical analysis
In socioeconomic areas, functional observations may be collected with weights, called weighted functional data. In this paper, we deal with a general linear hypothesis testing (GLHT) problem in the framework of functional analysis of variance with weighted functional data. With weights taken into account, we obtain unbiased and consistent estimators of the group mean and covariance functions. For the GLHT problem, we obtain a pointwise F ‐test statistic and build two global tests, respectively, via integrating the pointwise F ‐test statistic or taking its supremum over an interval of interest. The asymptotic distributions of test statistics under the null and some local alternatives are derived. Methods for approximating their null distributions are discussed. An application of the proposed methods to density function data is also presented. Intensive simulation studies and two real data examples show that the proposed tests outperform the existing competitors substantially in terms of size control and power.