Estimation and testing for partially linear single-index models.
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In partially linear single-index models, the semiparametrically efficient profile least-squares estimators of regression coefficients are obtained and a proposed tuning parameter selector, BIC, is demonstrated that identifies the true model consistently.Abstract:
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.read more
Citations
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References
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Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Jianqing Fan,Runze Li +1 more
TL;DR: In this article, penalized likelihood approaches are proposed to handle variable selection problems, and it is shown that the newly proposed estimators perform as well as the oracle procedure in variable selection; namely, they work as well if the correct submodel were known.
Book
Local polynomial modelling and its applications
Jianqing Fan,Irène Gijbels +1 more
TL;DR: Applications of Local Polynomial Modeling in Nonlinear Time Series and Automatic Determination of Model Complexity and Framework for Local polynomial regression.
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