Versions of Kernel-Type Regression Estimators
本文梳理了Gasser-Müller、Nadaraya-Watson和Priestley-Chao等核回归估计量的关系，指出随机设计下的不足，并介绍核加权局部线性拟合作为更优方法，适合希望理解核平滑器统一框架的学者。
Abstract We explore the aims of, and relationships between, various kernel-type regression estimators. To do so, we identify two general types of (direct) kernel estimators differing in their treatment of the nuisance density function associated with regressor variable design. We look at the well-known Gasser-Müller, Nadaraya-Watson, and Priestley-Chao methods 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 remedied by kernel-weighted local linear fitting, a well-known technique that is currently enjoying renewed popularity. We see how to fit this approach into our general framework, and hence form a unified understanding 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 motivated 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.