Variable selection in partial linear regression with functional covariate |
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Authors: | G Aneiros F Ferraty P Vieu |
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Institution: | 1. Departamento de Matemáticas, Universidad de A Coru?a, A Coru?a, Spainganeiros@udc.es;3. Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse, France |
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Abstract: | The problem of variable selection is considered in high-dimensional partial linear regression under some model allowing for possibly functional variable. The procedure studied is that of nonconcave-penalized least squares. It is shown the existence of a √n/sn-consistent estimator for the vector of pn linear parameters in the model, even when pn tends to ∞ as the sample size n increases (sn denotes the number of influential variables). An oracle property is also obtained for the variable selection method, and the nonparametric rate of convergence is stated for the estimator of the nonlinear functional component of the model. Finally, a simulation study illustrates the finite sample size performance of our procedure. |
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Keywords: | functional data highly increasing dimension partially linear modelling sparse model variable selection |
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