|
Abstract:
|
We propose a method of simultaneous model selection and estimation in additive regression models (ARMs) for continuous normal data. We use the mixed model representation of the smoothing spline estimators of the nonparametric functions in ARMs, where the importance of these functions is controlled by treating the inverse of the smoothing parameters as extra variance components. The selection is achieved by maximizing the penalized likelihood with the adaptive LASSO. A unified EM algorithm is provided to obtain the maximum penalized likelihood estimates of the nonparametric functions and the variance components. In the same model framework, we also consider forward selection based on score tests, and a two stage selection approach that imposes an early stage screening using individual score test on each variance component. The methods are illustrated with application to real data.
|
