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arXiv 2007.017572020-07math.STstat.TH

Monotonicity preservation properties of kernel regression estimators

Iosif Pinelis

备注：: A shorter version, without pictures, to appear in Statistics and Probability Letters

英文摘要：

Three common classes of kernel regression estimators are considered: the Nadaraya--Watson (NW) estimator, the Priestley--Chao (PC) estimator, and the Gasser--Müller (GM) estimator. It is shown that (i) the GM estimator has a certain monotonicity preservation property for any kernel $K$, (ii) the NW estimator has this property if and only the kernel $K$ is log concave, and (iii) the PC estimator does not have this property for any kernel $K$. Other related properties of these regression estimators are discussed.

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