Titlebook: Combinatorial Methods in Density Estimation; Luc Devroye,Gábor Lugosi Book 2001 Springer-Verlag New York, Inc. 2001 Density Estimation.Lik

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暗語(yǔ)

dithiolethione

枯燥

intention

Skeleton Estimates, in are totally bounded, that is, for every . > 0, there exists a finite number .. of densities in . such that the .. balls of radius . centered at these densities cover ., that is, if these chosen densities are .. = {.1,…,..}, then . where .. = {. : ∫ |. ? .| ≤ .}. The smallest such .. is called th

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The Minimum Distance Estimate: Examples,t the skeleton estimate defined in the previous chapter always works when . is totally bounded. In this chapter we analyze the minimum distance estimate described in Section 6.8. Assume that the densities .. ∈ . are indexed by a parameter . ∈ Θ.

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歡呼

Additive Estimates and Data Splitting,o construct a density estimate .. whose .. error is (almost) as small as that of the best estimate among the .., . ∈ Θ. Applying the minimum distance estimate of Chapter 5 directly to this class is often problematic because of the dependence of each estimate in the class and the empirical measure ..

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Multiparameter Kernel Estimates,almost optimal manner. The examples are all simple multiparameter versions of the kernel estimate. Once again, the methods applied here are fully combinatorial, as the only thing we need in each case is a suitable upper bound for the shatter coefficient appearing in Theorem 10.3.

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