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作者：Groeneboom, P; Jongbloed, G; Wellner, JA
作者单位：Delft University of Technology; Vrije Universiteit Amsterdam; University of Washington; University of Washington Seattle
摘要：A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively, We call this process the invelope and show that it is an almost surely uniquely defined function of integrated Brownian motion, Its role is comparable to the role of the greatest convex minorant of Brownian motion plus a parabolic drift in the problem of estimating monoto...
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作者：Ruckstuhl, AF; Welsh, AH
作者单位：Zurich University of Applied Sciences; University of Southampton
摘要：We consider the problem of robust inference for the binomial(m, pi) model. The discreteness of the data and the fact that the parameter and sample spaces are bounded mean that standard robustness theory gives surprising results. For example, the maximum likelihood estimator (MLE) is quite robust, it cannot be improved on for m = 1 but can be for m > 1. We discuss four other classes of estimators: M-estimators, minimum disparity estimators, optimal MGP estimators, and a new class of estimators ...
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作者：Johnstone, IM
作者单位：Stanford University
摘要：Let x((1)) denote the square of the largest singular value of an n x p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x((1)) is the largest principal component variance of the covariance matrix X'X, or the largest eigenvalue of a p-variate Wishart distribution on n degrees of freedom with identity covariance. Consider the limit of large p and n with n/p = gamma greater than or equal to 1. When centered by mu (p) = (rootn - 1 + rootp)(2) and scaled by s...
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作者：Klemelä, J; Tsybakov, AB
作者单位：Ruprecht Karls University Heidelberg; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider estimation of a linear functional T(f) where f is an unknown function observed in Gaussian white noise. We find asymptotically sharp adaptive estimators on various scales of smoothness classes in multidimensional situations, The results allow evaluating explicitly the effect of dimension and treating general scales of classes. Furthermore, we establish a connection between sharp adaptation and optimal recovery. Namely, we propose a scheme that reduces the construction of sharp adap...
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作者：Ghosal, S
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Mixture models for density estimation provide a very useful set up for the Bayesian or the maximum likelihood approach. For a density on the unit interval, mixtures of beta densities form a flexible model. The class of Bernstein densities is a much smaller subclass of the beta mixtures defined by Bernstein polynomials, which can approximate any continuous density. A Bernstein polynomial prior is obtained by putting a prior distribution on the class of Bernstein densities. The posterior distrib...
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作者：Shen, XT; Wasserman, L
作者单位：University System of Ohio; Ohio State University; Carnegie Mellon University
摘要：We compute the rate at which the posterior distribution concentrates around the true parameter value. The spaces we work in are quite general and include infinite dimensional cases. The rates are driven by two quantities: the size of the space, as measured by bracketing entropy, and the degree to which the prior concentrates in a small ball around the true parameter. We consider two examples.
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作者：Kuriki, S; Takemura, A
作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; University of Tokyo
摘要：Let Z be a k-way array consisting of independent standard normal variables. For column vectors h(1), ..., h(k), define a multilinear form of deg-ree k by (h(1) circle times . . . circle times h(k))'vec(Z). We derive formulas for upper tail probabilities of the maximum of a multilinear form with respect to the h(i)'s under the condition that the h(i)'s are unit vectors, and of its standardized statistic obtained by dividing by the norm of Z. We also give formulas for the maximum of a symmetric ...
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作者：Xu, HQ; Wu, CFJ
作者单位：University of Michigan System; University of Michigan
摘要：By studying treatment contrasts and ANOVA models, we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs. The criterion is independent of the choice of treatment contrasts and thus model-free. It works for symmetrical and asymmetrical designs, regular and nonregular designs. In particular, it reduces to the minimum aberration criterion for regular designs and the minimum G(2)-aberration criterion for two-level nonregular designs. In additi...
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作者：Bagchi, B; Bagchi, S
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore
摘要：We find a sufficient condition on the spectrum of a partial geometric design d* such that, when d* satisfies this condition, it is better (with respect to all convex decreasing optimality criteria) than all unequally replicated designs (binary or not) with the same parameters b, v, h as d*. Combining this with existing results, we obtain the following results: (i) For any q greater than or equal to 3, a linked block design with parameters b = q(2), = q(2)+q, k = q(2)-1 is optimal with respect ...
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作者：Beran, R
作者单位：University of California System; University of California Berkeley
