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February 2016 Estimation for single-index and partially linear single-index integrated models
Chaohua Dong, Jiti Gao, Dag Tjøstheim
Ann. Statist. 44(1): 425-453 (February 2016). DOI: 10.1214/15-AOS1372


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.


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Chaohua Dong. Jiti Gao. Dag Tjøstheim. "Estimation for single-index and partially linear single-index integrated models." Ann. Statist. 44 (1) 425 - 453, February 2016.


Received: 1 January 2015; Revised: 1 August 2015; Published: February 2016
First available in Project Euclid: 5 January 2016

zbMATH: 1331.62190
MathSciNet: MR3449774
Digital Object Identifier: 10.1214/15-AOS1372

Primary: 62G05 , 62G08 , 62G20

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

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 1 • February 2016
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