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作者：Grund, B; Hall, P
作者单位：Australian National University
摘要：We show that, for L(p) convergence of the mode of a nonparametric density estimator to the mode of an unknown probability density, finiteness of the pth moment of the underlying distribution is both necessary and sufficient. The basic requirement of existence of finite variance has been overlooked by statisticians, who have earlier considered mean square convergence of nonparametric mode estimators; they have focussed on mean squared error of the asymptotic distribution, rather than an asympto...
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作者：Gustafson, P; Wasserman, L
作者单位：Carnegie Mellon University
摘要：We investigate diagnostics for quantifying the effect of small changes to the prior distribution over a h-dimensional parameter space. We show that several. previously suggested diagnostics, such as the norm of the Frechet derivative, diverge at rate n(k/2) if the base prior is an interior point in the class of priors, under the density ratio topology. Diagnostics based on phi-divergences exhibit similar asymptotic behavior. We show that better asymptotic behavior can be obtained by suitably r...
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作者：Hall, P; Lahiri, SN; Polzehl, J
作者单位：Zuse Institute Berlin; Iowa State University
摘要：We analyse methods based on the block bootstrap and leave-out cross-validation, for choosing the bandwidth in nonparametric regression when errors have an almost arbitrarily long range of dependence. A novel analytical device for modelling the dependence structure of errors is introduced. This allows a concise theoretical description of the way in which the range of dependence affects optimal bandwidth choice. It is shown that, provided block length or leave-out number, respectively, are chose...
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作者：Stein, ML
摘要：For a stationary random field Z on R(d), this work studies the asymptotic behavior of predictors of integral v(x)Z(x) dx based on observations on a lattice as the distance between neighbors in the lattice tends to 0. Under a mild condition on the spectral density of Z, an asymptotic expression for the mean-squared error of a predictor of integral v(x)Z(x) dx based on observations on an infinite lattice is derived. For predicting integrals over the unit cube, a simple predictor based just on ob...
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作者：Dette, H; Wong, WK
作者单位：University of California System; University of California Los Angeles
摘要：We study properties of the variance function of the least squares estimator for the response surface. For polynomial models, we identify a class of approximate designs for which their Variance functions are maximized at the extreme points of the design space. As an application, we examine robustness properties of D-optimal designs and D-n-r-optimal designs under various polynomial model assumptions. Analytic formulas for the G-efficiencies of these designs are derived, along with their D-effic...
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作者：Cheng, C
摘要：Various smoothing methods for quantile density estimation are unified into a generalized kernel smoothing. Based on a stochastic upper bound of the derivatives sequence for a sequence of smoothed Brownian bridges, uniform in-probability consistency of generalized kernel quantile density estimators on any closed subinterval of the open unit interval is derived.
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作者：Prentice, MJ; Mardia, KV
作者单位：University of Leeds
摘要：This paper deals with the statistical analysis of matched pairs of shapes of configurations of landmarks in the plane. We provide inference procedures on the complex projective plane for a basic measure of shape change in the plane, on observing that shapes of configurations of (k + 1) landmarks in the plane may be represented as points on CPk-1 and that complex rotations are the only maps on CSk-1 which preserve the usual Hermitian inner product. Specifically, if u(1), ..., u(n) are fixed poi...
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作者：Stein, ML
摘要：For predicting integral(G)v(x)Z(x) dx, where v is a fixed known function and Z is a stationary random field, a good sampling design should have a greater density of observations where v is relatively large in absolute value. Designs using this idea when G = [0, 1] have been studied for some time. For G a region in two dimensions, very little is known about the statistical properties of cubature rules based on designs with varying density. This work proposes a class of designs that are locally ...
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作者：Drees, H
摘要：Consider a distribution function that belongs to the weak domain of attraction of an extreme value distribution. The extreme value index beta will be estimated by mixtures of Pickands estimators, where the weights are generated by a probability measure which satisfies a certain integrability condition. We prove a functional limit theorem for a process of Pickands estimators and asymptotic normality of the refined Pickands estimator. For negative beta the new estimator is asymptotically superio...
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作者：Clarke, B; Ghosh, JK
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：For various applications one wants to know the asymptotic behavior of w(theta\(X) over bar), the posterior density of a parameter theta given the mean (X) over bar of the data rather than the full data set. Here we show that w(theta\(X) over bar) is asymptotically normal in an L(1) sense, and rye identify the mean of the limiting normal and its asymptotic variance. The main results are first proved assuming that X(1),..., X(n),... are independent and identical; suitable modifications to obtain...
