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Activity Number:
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207
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Type:
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Topic Contributed
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Date/Time:
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Tuesday, August 13, 2002 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #300489 |
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Title:
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Penalized Spline Estimation for Partially linear Single-Index Models
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Author(s):
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Yan Yu*+ and David Ruppert
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Affiliation(s):
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University of Cincinnati and Cornell University
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Address:
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PO Box 210130, Cincinnati, Ohio, 45221-0130, USA
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Keywords:
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Asymptotics ; Consistency ; Dimension Reduction ; Inference ; Ridge Regression ; Sandwich Formula
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Abstract:
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Single-index models are an important tool for multivariate nonparametric regression. We propose penalized spline (P-spline) estimation of $\eta(\cdot)$ in partially linear single index models, where the mean function has the form $\eta({\alpha}^T\bx) + {\beta}^T \bz.$ The P-spline approach offers a number of advantages. All parameters in the P-spline single index model can be estimated simultaneously by penalized nonlinear least-squares. As a direct least-squares fitting method, our approach is rapid and computationally stable. Standard nonlinear least-squares software can be used. Moreover, joint inference for the parameters is possible by standard estimating equations theory. Using asymptotics where the number of knots is fixed though potentially large, we show $\sqrt{n}$-consistency and asymptotic normality of the estimators of all parameters. These asymptotic results permit joint inference for the parameters. Several examples illustrate that the model and proposed estimation methodology are effective in practice. We investigate inference based on the sandwich estimate through a Monte Carlo study. General $L_q$ penalty functions are also discussed.
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