Penalized spline estimation for functional coefficient regression models

Yanrong Cao, Haiqun Lin, Tracy Z. Wu and Yan Yu

Computational Statistics & Data Analysis, 2010, vol. 54, issue 4, 891-905

Abstract: The functional coefficient regression models assume that the regression coefficients vary with some "threshold" variable, providing appreciable flexibility in capturing the underlying dynamics in data and avoiding the so-called "curse of dimensionality" in multivariate nonparametric estimation. We first investigate the estimation, inference, and forecasting for the functional coefficient regression models with dependent observations via penalized splines. The P-spline approach, as a direct ridge regression shrinkage type global smoothing method, is computationally efficient and stable. With established fixed-knot asymptotics, inference is readily available. Exact inference can be obtained for fixed smoothing parameter [lambda], which is most appealing for finite samples. Our penalized spline approach gives an explicit model expression, which also enables multi-step-ahead forecasting via simulations. Furthermore, we examine different methods of choosing the important smoothing parameter [lambda]: modified multi-fold cross-validation (MCV), generalized cross-validation (GCV), and an extension of empirical bias bandwidth selection (EBBS) to P-splines. In addition, we implement smoothing parameter selection using mixed model framework through restricted maximum likelihood (REML) for P-spline functional coefficient regression models with independent observations. The P-spline approach also easily allows different smoothness for different functional coefficients, which is enabled by assigning different penalty [lambda] accordingly. We demonstrate the proposed approach by both simulation examples and a real data application.

Date: 2010
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Citations: View citations in EconPapers (5)

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