The Annals of Statistics

Estimation for single-index and partially linear single-index integrated models

Chaohua Dong, Jiti Gao, and Dag Tjøstheim

Full-text: Open access

Abstract

Estimation mainly for two classes of popular models, single-index and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link functions in the models and a profile approach is used to derive the estimators. The findings include the dual rate of convergence of the estimators for the single-index models and a trio of convergence rates for the partially linear single-index models. A new central limit theorem is established for a plug-in estimator of the unknown link function. Meanwhile, a considerable extension to a class of partially nonlinear single-index models is discussed in Section 4. Monte Carlo simulation verifies these theoretical results. An empirical study furnishes an application of the proposed estimation procedures in practice.

Article information

Source
Ann. Statist., Volume 44, Number 1 (2016), 425-453.

Dates
Received: January 2015
Revised: August 2015
First available in Project Euclid: 5 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.aos/1452004792

Digital Object Identifier
doi:10.1214/15-AOS1372

Mathematical Reviews number (MathSciNet)
MR3449774

Zentralblatt MATH identifier
1331.62190

Subjects
Primary: 62G05: Estimation 62G08: Nonparametric regression 62G20: Asymptotic properties

Keywords
Integrated time series orthogonal series expansion single-index models partially linear single-index models dual convergence rates a trio of convergence rates

Citation

Dong, Chaohua; Gao, Jiti; Tjøstheim, Dag. Estimation for single-index and partially linear single-index integrated models. Ann. Statist. 44 (2016), no. 1, 425--453. doi:10.1214/15-AOS1372. https://projecteuclid.org/euclid.aos/1452004792


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