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Penalized spline estimation for functional coefficient regression models
- Source :
-
Computational Statistics & Data Analysis . Apr2010, Vol. 54 Issue 4, p891-905. 15p. - Publication Year :
- 2010
-
Abstract
- 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 , 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 : 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 accordingly. We demonstrate the proposed approach by both simulation examples and a real data application. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 01679473
- Volume :
- 54
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Computational Statistics & Data Analysis
- Publication Type :
- Periodical
- Accession number :
- 47452817
- Full Text :
- https://doi.org/10.1016/j.csda.2009.09.036