Monotonicity preservation properties of kernel regression estimators
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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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