Abstract Kernel estimators with a global bandwidth are commonly used to estimate regression functions. On the other hand, it is obvious that the choice of a local bandwidth can lead to better results, because a larger class of kernel estimators is available. Evidently, this may in turn affect variability. The optimal bandwidths depend essentially on the regression function itself and on the residual variance, and it is desirable to estimate them from the data. In this article, a local bandwidth estimator is studied. A comparison with its global bandwidth equivalent is performed both in theory and in simulations. As the main result it is shown that the possible gain in mean integrated squared error of the resulting regression estimator must be paid for by a larger variability of the estimator. This may lead to worse results if the sample size is small. An algorithm has been devised that puts special weight on stability aspects. Our simulation study shows that improvements over a global bandwidth estimator often can be realized even at small or moderate sample sizes.
In the model $Y_i = g(t_i) + \\varepsilon_i,\\quad i = 1,\\cdots, n,$ where $Y_i$ are given observations, $\\varepsilon_i$ i.i.d. noise variables and $t_i$ nonrandom design poin...
Abstract We address the problem of smoothing parameter selection for nonparametric curve estimators in the specific context of kernel regression estimation. Call the "optimal ba...
SUMMARY A striking feature of curve estimation is that the smoothing parameter ĥ 0, which minimizes the squared error of a kernel or smoothing spline estimator, is very difficul...
Abstract An important aspect of nonparametric regression by spline smoothing is the estimation of the smoothing parameter. In this article we report on an extensive simulation s...
Summary Many different methods have been proposed to construct nonparametric estimates of a smooth regression function, including local polynomial, (convolution) kernel and smoo...
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