Three common classes of kernel regression estimators are considered: the Nadaraya--Watson (NW) estimator, the Priestley--Chao (PC) estimator, and the Gasser--M\"uller (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.

翻译：考虑了三种常见的内核回归估计值:Nadaraya-Watson(NW)估计值、Priestley-Chao(PC)估计值和Gasser-M\”uller(GM)估计值。 显示:(一) GM估计值对任何内核都具有某种单一性能保护财产,(二) NW估计值拥有这种财产,如果而且只有K$核心值是圆锥体,(三) PC估计值不拥有任何内核的这种财产,讨论这些回归估计值的其他有关特性。