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作者：BUJA, A; LOGAN, BF; REEDS, JA; SHEPP, LA
作者单位：AT&T; Nokia Corporation; Nokia Bell Labs
摘要：We solve the following variational problem: Find the maximum of E E\\X-Y\\ subject to E\\X\\2 less-than-or-equal-to 1, where X and Y are i.i.d. random n-vectors, and \\ . \\ is the usual Euclidean norm on R(n). This problem arose from an investigation into multidimensional scaling, a data analytic method for visualizing proximity data. We show that the optimal X is unique and is (1) uniform on the surface of the unit sphere, for dimensions n greater-than-or-equal-to 3, (2) circularly symmetric...
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作者：MASSAM, H
摘要：A class of exponential transformation models is defined on symmetric cones OMEGA with the group of automorphisms on OMEGA as the acting group. We show that these models are reproductive and the exponent of their joint distribution for a given sample of size q can be split into q independent components, introducing one sample point at a time. The automorphism group can be factorized into the group of positive dilation and another group. Accordingly, the symmetric cone OMEGA can be seen as the d...
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作者：STONE, CJ
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作者：TAKAGI, Y
摘要：Hajek established a local asymptotic minimax risk bound for appropriate symmetric loss functions and also gave a necessary condition for the risk of an estimator to attain the lower bound. We extend these results to the case of asymmetric loss functions. The asymmetry brings about the shift of location of the loss functions. Besides, the optimal estimator that attains the bound is shown to have asymptotic normal distribution with asymptotic bias.
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作者：DEMBO, A; PERES, Y
作者单位：Stanford University; University of California System; University of California Berkeley
摘要：A simple topological criterion is given for the existence of a sequence of tests for composite hypothesis testing problems, such that almost surely only finitely many errors are made.
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作者：PINELIS, I
摘要：We consider the Hotelling T2 statistic for an arbitrary d-dimensional sample. If the sampling is not too deterministic or inhomogeneous, then under the zero-means hypothesis the limiting distribution for T2 is chi(d)2. It is shown that a test for the orthant symmetry condition introduced by Efron can be constructed which does not differ essentially from the one based on chi(d)2 and at the same time is applicable not only to large random homogeneous samples but to all multidimensional samples. ...
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作者：LI, B; MCCULLAGH, P
作者单位：University of Chicago
摘要：A quasiscore function, as defined by Wedderbum and by McCullagh, frequently fails to have a symmetric derivative matrix Such a score function cannot be the gradient Of any Potential function on the parameter space; that is, there is no ''quasilikelihood.'' Without a likelihood function it is difficult to distinguish good roots from bad roots or to set satisfactory confidence limits. From a different perspective, a potential function seems to be essential in order to give the theory an approxim...
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作者：NABEYA, S; TANAKA, K
作者单位：Hitotsubashi University
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作者：NAGARAJA, HN; DAVID, HA
作者单位：Medical College of Wisconsin
摘要：For a random sample of size n from an absolutely continuous bivariate population (X,Y), let X(i:n) denote the ith order statistic of the X sample values. The Y-value associated with X(i:n) is denoted by Y([i:n]) and is called the concomitant of the ith order statistic. For 1 less-than-or-equal-to k less-than-or-equal-to n, let V(k,n) = Max(Y([n-k+1: n)],..., Y([n:n])). In this paper, we discuss the finite-sample and the asymptotic distributions of V(k,n). We investigate the limit distribution ...
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作者：JOHNSTONE, IM
摘要：Mallows has conjectured that among distributions which are Gaussian but for occasional contamination by additive noise, the one having least Fisher information has (two-sided) geometric contamination. A very similar problem arises in estimation of a nonnegative vector parameter in Gaussian white noise when it is known also that most [i.e., (1 - epsilon)) components are zero. We provide a partial asymptotic expansion of the minimax risk as epsilon --> 0. While the conjecture seems unlikely to b...
