On the Relationship between Stability of Extreme Order Statistics and Convergence of the Maximum Likelihood Kernel Density Estimate
نویسندگان
چکیده
Let f be a density on the real line and let f,~ be the kernel estimate of f in which the smoothing factor is obtained by maximizing the cross-validated likelihood product according to the method of Duin and Habbema, Hermans and Vandenbroek . Under mild regularity conditions on the kernel and f, we show, among other things that f Jf,~ f ( --~ 0 almost surely if and only if the sample extremes of f are strongly stable .
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