Hardle, W., Marron, J. S. and Wand, M. P. (1990). Bandwidth choice for density derivatives.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of f . As noted by Fan and Marron (1992) among the preceding selectors, only the selectors by Chiu (1991, 1992) 2 and by Hall et al. 1991) achieve the best possible constant coefficient B 2 0 (f ) and the others have larger constants, and hence are not optimal in this sense. For k 1, Hardle, Marron, and Wand (1990) proposed the cross validated bandwidth selector for (1.1) which has a slow convergence rate. Recently, Wu (1997) proposed two types of data based bandwidth selectors for (1.1) that achieve the best O p (n Gamma1=2 ) relative convergence rate to the optimal h k (f ) and, moreover, the ....

Hardle, W., Marron, J. S. and Wand, M. P. (1990). Bandwidth choice for density derivatives.

....K or n eff(K) observations and the optimal kernel K 0 . It turns out that for k = 2 most commonly used kernel have an efficiency of nearly 1 (Silverman, 1986, Chapter 3.3. 2) However, when estimating a density derivative f (p) by f (p) h the choice of the kernel plays an important role (Hardle, Marron, and Wand, 1990). Thus for practical reasons the choice of K is not as important as the choice of h. However, the same value of h gives for different kernel K a different amount of smoothing, i.e. the picture of f h (x) for the same h but different K will differ a lot. One method to make different kernels ....

Hardle, W., Marron, J.S., and Wand, M.P., Bandwidth Choice for Density Derivatives, Journal of the Royal Statistical Society, Series B, 52 (1990) 223--232.

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Hardle W., Marron J.S., and Wand M.P. (1990), "Bandwidth choice for density derivatives, " Journal of the Royal Statistical Society, Ser. B, 52, 223--232.

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