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作者：ELLIS, SP
摘要：Plane-fitting, for example, linear regression, principal components or projection pursuit, is treated from a general perspective. It is shown that any method of plane-fitting satisfying very mild hypotheses must have singularities, that is, data sets near which the procedure is unstable. The well-known collinearity phenomenon is least squares regression is a special case. Severity of singularities is also discussed. The results, which are applications of algebraic topology, may be viewed as pu...
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作者：LAI, TL; YING, ZL
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：A class of rank estimators is introduced for regression analysis in the presence of both left-truncation and right-censoring on the response variable. By making use of martingale theory and a tightness lemma for stochastic integrals of multiparameter empirical processes, the asymptotic normality of the estimators is established under certain assumptions. Adaptive choice of the score functions to give asymptotically efficient rank estimators is also discussed.
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作者：OSULLIVAN, F
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作者：MORGAN, JP; UDDIN, N
作者单位：Old Dominion University
摘要：Optimal and highly efficient two-dimensional designs are constructed for correlated errors on the torus and in the plane. The technique uses the method of differences to produce series of connectable planar squares. Efficiency calculations for planner versions of the torus designs show that the torus approximation is very satisfactory.
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作者：GEORGE, EI
摘要：Consider the problem of estimating the p X 1 mean vector theta-under expected squared error loss, based on the observation of two independent multivariate normal vectors Y1 approximately N(p)(theta, sigma-2I) and Y2 approximately N(p)(theta, lambda-sigma-2I) when lambda-and sigma-2 are unknown. For p greater-than-or-equal-to 3, estimators of the form delta-eta = eta-Y1 + (1 - eta)Y2 where-eta is a fixed number in (0,1), are shown to be uniformly dominated in risk by Stein estimators in spite o...
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作者：DATTA, S
摘要：The problem of finding admissible, asymptotically optimal compound rules is pursued in the infinite state case. The components involve the estimation of an arbitrary continuous transform of the natural parameter of a real exponential family with compact parameter space. We show that all Bayes estimators are admissible. Our main result is that any Bayes compound estimator versus a mixture of i.i.d. priors on the compound parameter is asymptotically optimal if the mixing hyperprior has full supp...
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作者：EVANS, M
摘要：Chaining, in combination with adaptive importance sampling, can provide an effective technique for the numerical evaluation of high-dimensional integrals in the context of a posterior analysis. In many statistical problems ways of applying chaining can be found which depend heavily on the structure of the problem. In this paper we consider a very general method of implementing chaining for arbitrary integrals. Also, we show that chaining can be applied to solve global optimization problems and...
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作者：CHU, CK; MARRON, JS
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：For nonparametric regression, in the case of dependent observations, cross-validation is known to be severely affected by dependence. This effect is precisely quantified through a limiting distribution for the cross-validated bandwidth. The performance of two methods, the leave-(2l + 1)-out version of cross-validation and partitioned cross-validation, which adjust for the effect of dependence on bandwidth selection is investigated. The bandwidths produced by these two methods are analyzed by f...
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作者：COMETS, F; GIDAS, B
作者单位：Brown University
摘要：We study the asymptotics of the ML estimators for the Curie-Weiss model parameterized by the inverse temperature beta and the external field h. We show that if both beta-and h are unknown, the ML estimator of (beta, h) does not exist. For beta-known, the ML estimator h triple-over-dot n of h exhibits, at a first order phase transition point, superefficiency in the sense that its asymptotic variance is half of that of nearby points. At the critical point (beta = 1), if the true value is h = 0, ...
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作者：SHI, XQ
摘要：This note studies the asymptotic behavior of the delete-d jackknife in the irregular case of a sample p-quantile, calculated from a sample of n iid r.v.'s. Two results are obtained: (a) an almost sure rate of convergence of the delete-d jackknife histogram to the normal distribution; (b) almost sure convergence of the delete-d jackknife variance estimate to the asymptotic variance of the sample p-quantile.
