Abstract
In the case of the fixed design nonparametric regression, the kernel estimator proposed by Gasser and Mueller (1979, 1984) is one of the most widely used regression smoothers. However, if some design points are closer to their neighbors than others are, then there is a drawback to the Gasser-Mueller estimator (GME). The drawback is that the variance of the GME will be increased by the too close design points. In the case of the jittered equidistant design, this effect is precisely quantified through the asymptotic mean square error (AMSE) of the GME. In this case, to overcome the effect, a new version of the GME is proposed. The AMSE of the new version of the GME is the same as that of the GME in the case of the equidistant design. Hence, in the jittered equidistant design case, the new version of the GME is of better performance than the GME, in the sense of minimum integrated mean square error. Simulations demonstrate that the asymptotic effects hold for reasonable sample sizes.
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