Wavelet Estimation of Partially Linear Models
Document Type
Article
Publication Date
8-1-2004
Abstract
A wavelet approach is presented for estimating a partially linear model (PLM). We find an estimator of the PLM by minimizing the square of the l2 norm of the residual vector while penalizing the l1 norm of the wavelet coefficients of the nonparametric component. This approach, an extension of the wavelet approach for nonparametric regression problems, avoids the restrictive smoothness requirements for the nonparametric function of the traditional smoothing approaches for PLM, such as smoothing spline, kernel and piecewise polynomial methods. To solve the optimization problem, an efficient descent algorithm with an exact line search is presented. Simulation results are given to demonstrate effectiveness of our method.
Publication Information
Chang, Xiao-Wen and Qu, Leming. (2004). "Wavelet Estimation of Partially Linear Models". Computational Statistics & Data Analysis, 47(1), 31-48. https://doi.org/10.1016/j.csda.2003.10.018
Comments
Erratum in: Computational Statistics & Data Analysis, 2005 April 1, 48(4), 677. Significant correction made to incorrectly printed text on page 42. See erratum publication for details at doi: 10.1016/j.csda.2004.10.002