This article provides an introduction to the major types of nonparametric regression techniques, including kernel, spline and orthogonal projection methods. Practical aspects of the methods and their applicability in environmental statistics are emphasized through examples and discussion. Topics covered include bandwidth selection, non-parametric regression in multiple dimensions, and methods f...

Definition A nonparametric procedure is a statistical procedure that has certain desirable properties that hold under relatively mild assumptions regarding the underlying population(s) from which the data are obtained – Hollander and Wolfe. The definition is not only vague but it is also extremely inclusive. “Statistical procedure” can refer to a test or an estimator. There are a number of new ...

Notes for the course by Bas Kleijn, Aad van der Vaart, Harry van Zanten (Text partly extracted from a forthcoming book by S. Ghosal and A. van der Vaart) version 4-12-2012 UNDER CONSTRUCTION 1 Introduction Why adopt the nonparametric Bayesian approach for inference? The answer lies in the simultaneous preference for nonparametric modeling and desire to follow a Bayesian procedure. Nonparametric...

We establish the √ n asymptotic equivalence of V and U statistics when the statistic’s kernel depends on n. Combined with a lemma of B. Lee this result provides conditions under which U statistics projections and V statistics are √ n asymptotically equivalent. The use of this equivalence in nonparametric regression models is illustrated with several examples; the estimation of conditional varia...

BACKGROUND Based on death certificate data, the Texas Department of Health Bureau of Vital Statistics calculates age adjusted all-cause mortality rates for each Texas county yearly. In 1998 the calculated rates for two adjacent Texas counties was disparate. These counties contain one city (Amarillo) and are identical in size. This study examined the accuracy of recorded county of residence for ...