VERSIONS OF KERNEL-TYPE REGRESSION-ESTIMATORS

We explore the aims of, and relationships between, various kernel-type regression estimators. To do so, we identify two general types of (di rect) kernel estimators differing in their treatment of the nuisance d ensity function associated with regressor variable design. We look at the well-known Gasser-Muller, Nadaraya-Watson, and Priestley-Chao meth ods in this light. In the random design case, none of these methods is totally adequate, and we mention a novel (direct) kernel method with appropriate properties. Disadvantages of even the latter idea are reme died by kernel-weighted local linear fitting, a well-known technique t hat is currently enjoying renewed popularity. We see how to fit this a pproach into our general framework, an hence form a unified understand ing of how these kernel type smoothers interrelate. Though the mission of this article is unificatory (and even pedagogical), the desire for better understanding of superficially different approaches is motivat ed by the need to improve practical estimators. In the end, we concur with other authors that kernel-weighted local linear fitting deserves much further attention for applications.