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Title: Semi-parametric estimation of partially linear single-index models
Authors: Xia, Y. 
Härdle, W.
Keywords: Asymptotic distribution
Generalized partially linear model
Local linear smoother
Optimal consistency rate
Single-index model
Issue Date: May-2006
Source: Xia, Y., Härdle, W. (2006-05). Semi-parametric estimation of partially linear single-index models. Journal of Multivariate Analysis 97 (5) : 1162-1184. ScholarBank@NUS Repository.
Abstract: One of the most difficult problems in applications of semi-parametric partially linear single-index models (PLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot estimators are often assumed to be root- n consistent, although they are not given in a constructible way. Complexity parameters, such as a smoothing bandwidth are constrained to a certain speed, which is rarely determinable in practical situations. In this paper, efficient, constructible and practicable estimators of PLSIMs are designed with applications to time series. The proposed technique answers two questions from Carroll et al. [Generalized partially linear single-index models, J. Amer. Statist. Assoc. 92 (1997) 477-489]: no root- n pilot estimator for the single-index part of the model is needed and complexity parameters can be selected at the optimal smoothing rate. The asymptotic distribution is derived and the corresponding algorithm is easily implemented. Examples from real data sets (credit-scoring and environmental statistics) illustrate the technique and the proposed methodology of minimum average variance estimation (MAVE). © 2005 Elsevier Inc. All rights reserved.
Source Title: Journal of Multivariate Analysis
ISSN: 0047259X
DOI: 10.1016/j.jmva.2005.11.005
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