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Lasso estimation for spherical autoregressive processes. (English) Zbl 1467.62126

Summary: The purpose of the present paper is to investigate a class of spherical functional autoregressive processes in order to introduce and study LASSO (Least Absolute Shrinkage and Selection Operator) type estimators for the corresponding autoregressive kernels, defined in the harmonic domain by means of their spectral decompositions. Some crucial properties for these estimators are proved, in particular, consistency and oracle inequalities.

MSC:

62J07 Ridge regression; shrinkage estimators (Lasso)
62M15 Inference from stochastic processes and spectral analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M40 Random fields; image analysis
62R10 Functional data analysis
60G15 Gaussian processes
60G60 Random fields
60F05 Central limit and other weak theorems

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