Journal of Statistics: Advances in Theory and ApplicationsAuthor's: Takuma Yoshida
Pages: [125] - [166]
Received Date: October 2, 2015
Submitted by:
DOI: http://dx.doi.org/10.18642/jsata_7100121548
This paper studies the problem of flexible estimation and variable selection in partial linear models. We estimate the parameters and smooth function in the literature of the robust regression with M-estimation. First, we use the radial basis function model to estimate the smooth function. For the nonlinear component, it is known that the ordinary M-estimation leads to obtain an over fitted curve. To overcome this, we propose the new estimation method using the sufficient dimension reduction (SDR) method. First, the SDR methods to radial basis functions are applied for trying to find small number of linear combinations of the radial bases without loss of information in the regression. Second, a multiple linear regression model between a response and the transformed radial bases is assumed and ordinary M-estimation is provided. As the result, using the proposed method, the variance reduction can be achieved and hence it avoids the over fitting. In the parametric component, on the other hand, we practice the variable selection using the penalization methods, such as Lasso, SCAD, and Adaptive Lasso. The theoretical justification is proved and simulation results are given. Real data examples are also addressed.
partial linear model, sufficient dimension reduction, thin plate spline, variance reduction, variable selection.
