共查询到20条相似文献,搜索用时 15 毫秒
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Given a density f we pose the problem of estimating the density functional $\psi_r=\int f^{(r)}f$ for a non-negative even r making use of kernel methods. This is a well-known problem but some of its features remained unexplored. We focus on the problem of bandwidth selection. Whereas all the previous studies concentrate on an asymptotically optimal bandwidth here we study the properties of exact, non-asymptotic ones, and relate them with the former. Our main conclusion is that, despite being asymptotically equivalent, for realistic sample sizes much is lost by using the asymptotically optimal bandwidth. In contrast, as a target for data-driven selectors we propose another bandwidth which retains the small sample performance of the exact one. 相似文献
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Dean Baskin 《Annales Henri Poincare》2013,14(2):221-252
In this article we prove a family of local (in time) weighted Strichartz estimates with derivative losses for the Klein–Gordon equation on asymptotically de Sitter spaces and provide a heuristic argument for the non-existence of a global dispersive estimate on these spaces. The weights in the estimates depend on the mass parameter and disappear in the “large mass” regime. We also provide an application of these estimates to establish small-data global existence for a class of semilinear equations on these spaces. 相似文献
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本文获得了刻度指数族变量带误差情形下的贝叶斯决策,且利用解卷积的核方法构造出了经验贝叶斯决策.在适当的条件下,证明了经验贝叶斯决策的渐近最优性. 相似文献
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《Journal of Complexity》1998,14(1):34-48
We study numerical integration of Hölder-type functions with respect to weights on the real line. Our study extends previous work by F. Curbera (J. Complexity14(1), (1998) and relies on a connection between this problem and the approximation of distribution functions by empirical ones. As an application we reproduce a variant of the well-known result for weighted integration of Brownian paths. 相似文献
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Jean-Marc Bouclet 《Annales Henri Poincare》2006,7(3):527-561
Combining results of Cardoso-Vodev [6] and Froese-Hislop [9], we use Mourre’s theory to prove high energy estimates for the
boundary values of the weighted resolvent of the Laplacian on an asymptotically hyperbolic manifold. We derive estimates involving
a class of pseudo-differential weights which are more natural in the asymptotically hyperbolic geometry than the weights
used in [6].
submitted 28/04/05, accepted 26/09/05 相似文献
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Jean-Marc Bouclet 《偏微分方程通讯》2013,38(7):1239-1286
For Riemannian metrics G on ? d which are long range perturbations of the flat one, we prove estimates for (? Δ G ? λ ?iε)?n as λ → 0, which are uniform with respect to ε, for all n ≤ [d/2] +1 in odd dimension and n ≤ d/2 in even dimension. We also give applications to the time decay of Schrödinger and Wave (or Klein–Gordon) equations. 相似文献
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Radu Păltănea 《Results in Mathematics》1997,32(3-4):318-331
In this paper we obtain estimates with optimal constants for the pointwise approximation of functions by linear positive functional, with the aid of a new second order modulus with a parameter, as well as with the aid of the first order modulus of the derivatives of functions. 相似文献
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Multivariate kernel density estimators are known to systematically deviate from the true value near critical points of the density surface. To overcome this difficulty a method based on Rao–Blackwell's theorem is proposed. Local corrections of kernel density estimators are achieved by conditioning these estimators with respect to locally sufficient statistics. The asymptotic as well as the small sample size behavior of the improved estimators are studied. Asymptotic bias and variance are investigated and weak and complete consistency are derived under mild hypothesis. 相似文献
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Arnak S. Dalalyan Yury A. Kutoyants 《Statistical Inference for Stochastic Processes》2003,6(1):89-107
The problem of estimation of the derivative of the invariant density is considered for a one-dimensional ergodic diffusion process. The lower minimax bound on the L
2-type risk of all estimators is proposed and an asymptotically efficient (up to the constant) in the sense of this bound kernel-type estimator is constructed. 相似文献
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A sequential asymptotically efficient procedure is constructed for estimating the drift coefficient at a given state point
in ergodic diffusion processes. Sequential kernel estimators are used. The optimal convergence rate with the sharp constant
is given for a local minimax risk. 相似文献
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Yang Zhenai 《数学年刊B辑(英文版)》1990,11(4):536-545
Let be the collection of m-times continuously differentiable probability densities fon R~d such that 丨D~af(x_1)-D~af(x_2)丨≤M‖x_1-x_2‖~β for x_1,x_2∈R~d,[a]=m,where D~adenotes the differential operator defined by D~a=([a])/(x_1~a…x_d~a_d).Under rather weak conditionson K(x),the necessary and sufficient conditions for sup丨_n(x)-f(x)丨=0(((logn/n)~λ/(d+3λ),λ=m+β,f∈ are that ∫x~aK(xi)dx=0 for 0<[a]≤m.Finally the convergenco rate at apoint is given. 相似文献
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《Journal of computational and graphical statistics》2013,22(2):372-397
This article introduces graphical tools for visualizing multivariate functions, specializing to the case of visualizing multivariate density estimates. We visualize a density estimate by visualizing a series of its level sets. From each connected part of a level set a shape tree is formed. A shape tree is a tree whose nodes are associated with regions of the level set. With the help of a shape tree we define a transformation of a multivariate set to a univariate function. The shape trees are visualized with the shape plots and the location plot. By studying these plots one may identify the regions of the Euclidean space where the probability mass is concentrated. An application of shape trees to visualize the distribution of stock index returns is presented. 相似文献
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Suppose that X1,…,Xn are samples drawn from a in-dimensional population with probability density function f belonging to a family Ckα(where k is a given positive integer, and α is a given positive number) defined as follows: f∈Ckα if and only if. 相似文献
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The problem of the nonparametric minimax estimation of an infinitely smooth density at a given point, under random censorship, is considered. We establish the exact asymptotics of the local minimax risk and propose the efficient kernel-type estimator based on the well known Kaplan-Meier estimator. 相似文献