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Wavelet estimation of the dimensionality of curve time series. (English) Zbl 1465.62148

Summary: Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among other principles, have been used to tackle this issue. We discuss here a solution based on a finite-dimensional functional subspace. We employ wavelet representation of random functions to estimate this finite dimension and successfully model a time series of curves. The proposed method is shown to have nice asymptotic properties. Moreover, the wavelet representation permits the use of several bootstrap procedures, and it results in faster computing algorithms. Besides the theoretical and computational properties, some simulation studies and an application to real data are provided.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F40 Bootstrap, jackknife and other resampling methods
62R10 Functional data analysis
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
62P10 Applications of statistics to biology and medical sciences; meta analysis
92B15 General biostatistics

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