Open Access
May 2020 Efficient estimation in single index models through smoothing splines
Arun K. Kuchibhotla, Rohit K. Patra
Bernoulli 26(2): 1587-1618 (May 2020). DOI: 10.3150/19-BEJ1183


We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth link function. We develop a method to compute the penalized least squares estimators (PLSEs) of the parametric and the nonparametric components given independent and identically distributed (i.i.d.) data. We prove the consistency and find the rates of convergence of the estimators. We establish asymptotic normality under mild assumption and prove asymptotic efficiency of the parametric component under homoscedastic errors. A finite sample simulation corroborates our asymptotic theory. We also analyze a car mileage data set and a Ozone concentration data set. The identifiability and existence of the PLSEs are also investigated.


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Arun K. Kuchibhotla. Rohit K. Patra. "Efficient estimation in single index models through smoothing splines." Bernoulli 26 (2) 1587 - 1618, May 2020.


Received: 1 May 2019; Revised: 1 October 2019; Published: May 2020
First available in Project Euclid: 31 January 2020

zbMATH: 07166575
MathSciNet: MR4058379
Digital Object Identifier: 10.3150/19-BEJ1183

Keywords: Least favorable submodel , penalized least squares , Semiparametric model

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 2 • May 2020
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