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Robust estimation and selection for single-index regression model. (English) Zbl 07193787

Summary: In this paper, we consider a single-index regression model for which we propose a robust estimation procedure for the model parameters and an efficient variable selection of relevant predictors. The proposed method is known as the penalized generalized signed-rank procedure. Asymptotic properties of the proposed estimator are established under mild regularity conditions. Extensive Monte Carlo simulation experiments are carried out to study the finite sample performance of the proposed approach. The simulation results demonstrate that the proposed method dominates many of the existing ones in terms of robustness of estimation and efficiency of variable selection. Finally, a real data example is given to illustrate the method.

MSC:

62J02 General nonlinear regression
62G05 Nonparametric estimation
62F12 Asymptotic properties of parametric estimators
62G20 Asymptotic properties of nonparametric inference
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