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Estimation and testing for partially linear single-index models. (English) Zbl 1204.62068
Summary: In partially linear single-index models, we obtain the semiparametrically efficient profile least-squares estimators of regression coefficients. We also employ the smoothly clipped absolute deviation penalty (SCAD) approach to simultaneously select variables and estimate regression coefficients. We show that the resulting SCAD estimators are consistent and possess the oracle property. Subsequently, we demonstrate that a proposed tuning parameter selector, BIC, identifies the true model consistently. Finally, we develop a linear hypothesis test for the parametric coefficients and a goodness-of-fit test for the nonparametric component, respectively. Monte Carlo studies are also presented.

MSC:
62G08 Nonparametric regression and quantile regression
62G10 Nonparametric hypothesis testing
62J05 Linear regression; mixed models
65C05 Monte Carlo methods
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