Asymptotic Behavior of a Kernel Regression Estimator with Random Predictor Variable

Wann-Jyi Horng


The almost sure limiting behavior and convergence rate of a kernel regression estimator are studied. As the domain of density function is compactly supported, it is known that the regression estimator of Mack and Muller [11] will also encounter the problem of the boundary effects, that is, it lacks the consistency property. In order to improve the limiting behavior and convergence rate as above, the idea of linear-fit method is used to construct a general weighted kernel regression estimator. In this paper, the almost sure limiting behavior, the convergence rate and some properties of the proposed estimator are given. Besides, the proposed estimator does not also need to adjust the boundary regions.


Kernel regression estimator, Boundary effects, Bandwidth, Convergence rate


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