Abstract
In this paper, we develop an asymptotic χ2 test for detecting differences among mean functions when sparse and irregular observations are drawn from the underlying continuous stochastic processes for each subject. We provide theoretical arguments to justify the effectiveness of the proposed test procedure. Numerical experiments, including simulation studies and applications to a CD4 count data set and an eBay online auction data set, are presented to demonstrate the good performance of the developed test.
Highlights
Functional data refers to data drawn from continuous underlying processes
Consider nine tests: the proposed asymptotic χ2 test (‘Shrink Hotelling’), the distribution test (‘Dist’), the linear and cubic pLRT test (‘pLRT-l’, ‘pLRT-c’), the dense-recovered tests (‘normalized l2’, ‘Globalized-F test [42] (GF)’, ‘l2’), and the dense-recovered tests based on 5000 Monte Carlo permutations (‘normalized l2-pm’, ‘GF-pm’, ‘l2-pm’)
We developed an asymptotic χ2 test for detecting differences among the mean functions of two independent stochastic processes with homogeneous covariance functions, when only a few irregularly spaced measurements are given for each subject
Summary
Functional data refers to data drawn from continuous underlying processes. Examples include time series, image data, and tracing data such as hand-writings. We propose a Hotelling’s T 2 type statistic based on a shrinkage eigen-projection score vector This is an alternative way of extending the sparse FPC in [40] to multiple groups of sparse functional data, in addition to the marginal FPC in [32]. The main results for the two-sample mean testing problem for sparse functional data, including the problem settings, the proposed test procedure, the corresponding asymptotic results, and an extension to common principal component cases, are stated in Sections 2 and 3.
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