On semiparametric regression via wavelets

Leming Qu, Purdue University

Abstract

Semiparametric regression models have a linear part as in the linear regression and a nonlinear part similar to that in the nonparametric regression. The estimates in semiparametric regression models have been studied previously in traditional smoothing methods such as smoothing spline, kernel and piecewise polynomial smoothers. In this thesis, we apply the regularized wavelet estimators by penalizing the l1 norm of the wavelet coefficients of the nonparametric function. The regularization parameter is chosen by universal threshold or cross-validation. When there is only one explanatory variable in the linear part, we directly solve the linear coefficient. When the linear part has multivariate predictors, we developed an iterative algorithm similar to backfitting. Simulation results show that regularized wavelet approach performs well. We also approached the problem from the Bayesian perspective by posing a prior of mixture of normal and a point mass at 0 on the wavelet coefficients.

Degree

Ph.D.

Advisors

Bock, Purdue University.

Subject Area

Mathematics|Statistics

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