![]() ![]() The data and the curve‐estimate, where you choose by the trial-bandwidth slider, show that the choice of the bandwidth is crucial.Ģ. Here six examples for (the "true curve") can be tried: is plotted (in blue) in the third of the three possible views using the tabs:ġ. Notice that GCV (in contrast to the method) does not require that be known. See for a review and see for the definition and an analysis of. In fact, cross‐validation and GCV coincide in our context, where periodic end conditions are assumed. Three very popular methods are available for choosing : cross‐validation (also called the "leave‐one‐out" principle see PRESS statistic), generalized cross validation (GCV), and Mallows’ (also sometimes denoted by or UBR for unbiased risk estimate). Notice that depends on, , and the 's only through the data. The curve estimate corresponding to a given value for the bandwidth parameter is then denoted. ![]() For the kernel method, it is known that choosing a good value for the famous bandwidth parameter (see Details) is crucial, much more than the choice of the class of the kernels, which is fixed here. In the kernel‐smoothing method (like in any similar nonparametric method, e.g. the smoothing spline method) one or several smoothing parameters have to be appropriately chosen to obtain a "good" estimate of the true curve. Perhaps the simplest "solution" to this problem is by the classical and widely used kernel‐smoothing method, which is a particular case of the Loess method (locally weighted scatterplot smoothing) see the Details below. ![]()
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