论文标题
内核回归估计器的单调性保存特性
Monotonicity preservation properties of kernel regression estimators
论文作者
论文摘要
考虑了三个常见的内核回归估计器：Nadaraya-Watson（NW）估计器，Priestley-Chao（PC）估算器和Gasser-Müller（GM）估计器。结果表明，（i）通用汽车估计器对任何内核$ k $具有一定的单调保存属性，（ii）NW估算器具有此属性IF and and and gernel $ k $是log凹室，并且（iii）PC估计器对任何kernel $ k $都不具有此属性。讨论了这些回归估计器的其他相关属性。
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.
