Data adaptive ridging in local polynomial regression

When estimating a regression function or its derivatives, local polynomials are art attractive choice due to their flexibility and asymptotic performa nce. Seifert and Gasser proposed ridging of local polynomials to overcome p roblems with variance for random design while retaining their advantages. I n this article we present a data-independent rule of thumb and a data-adapt ive spatial choice of the ridge parameter in local linear regression. In a framework of penalized local least squares regression, the methods are gene ralized to higher order polynomials, to estimation of derivatives, and to m ultivariate designs. The main message is that ridging is a powerful tool fo r improving the performance of local polynomials. A rule of thumb offers dr astic improvements; data-adaptive ridging brings further but modest gains i n mean square error.