Physical Sciences and Mathematics Commons^™

Local Adaptive Smoothing In Kernel Regression Estimation, Qi Zheng

All Theses

We consider nonparametric estimation of a smooth regression function of one variable. In practice it is quite popular to use the data to select one global smoothing parameter. Such global selection procedures cannot sufficiently account for local sparseness of the covariate nor can they adapt to local curvature of the regression function. We propose a new method to select local smoothing parameters which takes into account sparseness and adapts to local curvature of the regression function. A Bayesian method allows the smoothing parameter to adapt to the local sparseness of the covariate and provides the basis for a local cross …