Journal
JOURNAL OF NONPARAMETRIC STATISTICS
Volume 12, Issue 4, Pages 503-538Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/10485250008832820
Keywords
functional principal component analysis; nonparametric regression; rates of convergence; mean square error; asymptotic expansion; hybrid splines; B-splines
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This study deals with the simultaneous nonparametric estimations of n curves or observations of a random process corrupted by noise in which sample paths belong to a finite dimension functional subspace. The estimation, by means of B-splines, leads to a new kind of functional principal components analysis. Asymptotic rates of convergence are given for the mean and the eigenelements of the empirical covariance operator. Heuristic arguments show that a well chosen smoothing parameter may improve the estimation of the subspace which contains the sample path of the process. Finally, simulations suggest that the estimation method studied here is advantageous when there are a small number of design points.
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