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作者：DASGUPTA, A; GHOSH, JK; ZEN, MM
作者单位：National Cheng Kung University; Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：Let X have a star unimodal distribution P-0 on R(p). We describe a general method for constructing a star-shaped set S with the property P-0(X is an element of S) greater than or equal to 1 - alpha, where 0 < alpha < 1 is fixed. This is done by using the Camp-Meidell inequality on the Minkowski functional of an arbitrary star-shaped set S and then minimizing Lebesgue measure in order to obtain size-efficient sets. Conditions are obtained under which this method reproduces a level (high density...
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作者：ERICKSON, RV; FABIAN, V; MARIK, J
作者单位：Michigan State University
摘要：An optimum design of experiment for a class of estimates of the first derivative at 0 (used in stochastic approximation and density estimation) is shown to be equivalent to the problem of finding a point of minimum of the function Gamma defined by Gamma(x) = det[1, x(3), ..., x(2m-1)]/det[x, x(3), ..., x(2m-1)] on the set of all m-dimensional vectors with components satisfying 0 < x(1) < -x(2) < ... < (-1)(m-1)x(m) and Pi\x(i)\ = 1. (In the determinants, 1 is the column vector with all compone...
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作者：OSULLIVAN, F
摘要：Positron emission tomography (PET) is a radiologic tool offering a unique capability for measuring tissue metabolism in vivo. A number of biological and physical factors limit the resolution of PET so often the statistical aspects of image reconstruction have an appreciable effect on the quality of information obtained from a study. To a first approximation, reconstruction involves the solution of a linear inverse problem with a line-integral Radon-type transform. Standard filtered back-projec...
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作者：LIU, HM; BERGER, RL
作者单位：North Carolina State University
摘要：Let X have a multivariate, p-dimensional normal distribution(p greater than or equal to 2) with unknown mean mu and known, nonsingular covariance Sigma. Consider testing H-0:b(i)'mu less than or equal to 0, for some i = 1,..., k, versus H-1:b(i)'mu > 0, for all i = 1,..., k, where b(1),...,b(k), k greater than or equal to 2, are known vectors that define the hypotheses. For any 0 < alpha < 1/2, we construct a size-alpha test that is uniformly more powerful than the size-alpha likelihood ratio ...
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作者：VALZ, PD; MCLEOD, AI; THOMPSON, ME
作者单位：Western University (University of Western Ontario); University of Waterloo
摘要：Robillard's approach to obtaining an expression for the cumulant generating function of the null distribution of Kendall's S-statistic, when one ranking is tied, is extended to the general case where both rankings are tied. An expression is obtained for the cumulant generating function and it is used to provide a direct proof of the asymptotic normality of the standardized score, S/root Var(S), when both rankings are tied. The third cumulant of S is derived and an expression for exact evaluati...
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作者：Arcones, MA
摘要：The order of the Kolmogorov-Smirnov distance for the bootstrap of U-quantiles is considered. We observe that the order of the bootstrap of U-quantiles depends on the order of the local variance of the first term of the Hoeffding decomposition at the U-quantile. This order can be smaller than the order of the bootstrap of quantiles: U-quantiles can be smoother than quantiles.
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作者：KOROSTELEV, AP; SIMAR, L; TSYBAKOV, AB
作者单位：Universite Catholique Louvain; Sorbonne Universite
摘要：Let g: [0,1] --> [0,1] be a monotone nondecreasing function and let G be the closure of the set {(x, y) is an element of [0,1] X [0,1]: 0 less than or equal to y less than or equal to g(x)}. We consider the problem of estimating the set G from a sample of i.i.d. observations uniformly distributed in G. The estimation error is measured in the Hausdorff metric. We propose the estimator which is asymptotically efficient in the minimax sense.
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作者：Ghosal, S; Ghosh, JK; Samanta, T
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：A general (asymptotic) theory of estimation was developed by Ibragimov and Has'minskii under certain conditions on the normalized likelihood ratios. In an earlier work, the present authors studied the limiting behaviour of the posterior distributions under the general setup of Ibragimov and Has'minskii. In particular, they obtained a necessary condition for the convergence of a suitably centered (and normalized) posterior to a constant limit in terms of the limiting likelihood ratio process. I...
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作者：KULKARNI, SR; ZEITOUNI, O
作者单位：Technion Israel Institute of Technology; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Lincoln Laboratory
摘要：We consider the composite hypothesis testing problem of classifying an unknown probability distribution based on a sequence of random samples drawn according to this distribution. Specifically, if A is a subset of the space of all probability measures M(1)(Sigma) over some compact Polish space Sigma, we want to decide whether or not the unknown distribution belongs to A or its complement. We propose an algorithm which leads a.s. to a correct decision for any A satisfying certain structural ass...
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作者：LI, G; DOSS, H
作者单位：University System of Ohio; Ohio State University
摘要：Most hazard regression models in survival analysis specify a given functional form to describe the influence of the covariates on the hazard rate. For instance, Cox's model assumes that the covariates act multiplicatively on the hazard rate, and Aalen's additive risk model stipulates that the covariates have a linear additive effect on the hazard rate. In this paper we study a fully nonparametric model which makes no assumption on the association between the hazard rate and the covariates. We ...
