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作者：YANG, RY; BERGER, JO
摘要：Estimation of a covariance matrix Sigma is a notoriously difficult problem; the standard unbiased estimator can be substantially suboptimal. We approach the problem from a noninformative prior Bayesian perspective, developing the reference noninformative prior for a covariance matrix and obtaining expressions for the resulting Bayes estimators. These expressions involve the computation of high-dimensional posterior expectations, which is done using a recent Markov chain simulation tool, the hi...
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作者：SUN, JY; LOADER, CR
作者单位：Nokia Corporation; Nokia Bell Labs; AT&T
摘要：Suppose we observe Y-i = f(x(i)) + epsilon(i), i = 1,...,n. We wish to find approximate 1-alpha simultaneous confidence regions for {f(x), x is an element of x}. Our regions will he centered around linear estimates ($) over cap(x) of parametric or nonparametric f(x). There is a large amount of previous work on this subject. Substantial restrictions have been usually placed on some or all of the dimensionality of x, the class of functions f that can be considered, the class of linear estimates ...
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作者：LAI, TL; YING, ZL
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：A general missing information principle is proposed for constructing M-estimators of regression parameters in the presence df left truncation and right censoring on the observed responses. By making use of martingale central limit theorems and empirical process theory, the asymptotic normality of M-estimators is established under certain assumptions. Asymptotically efficient M-estimators are also developed by using data-dependent score functions. In addition, robustness properties of the estim...
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作者：CRITCHLEY, F; MARRIOTT, P; SALMON, M
作者单位：University of Surrey; European University Institute
摘要：A new preferred point geometric structure for statistical analysis, closely related to Amari's alpha-geometries, is introduced. The added preferred point structure is seen to resolve the problem that divergence measures do not obey the intuitively natural axioms for a distance function as commonly used in geometry. Using this tool, two key results of Amari which connect geodesics and divergence functions are developed. The embedding properties of the Kullback-Leibler divergence are considered ...
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作者：CHATTOPADHYAY, MK
摘要：Sequential selections are to be made from two independent stochastic processes, or ''arms.'' At each stage we choose which arm to observe based on past selections and observations. The observations on arm i are conditionally i.i.d. given their marginal distribution P-i which has a Dirichlet process prior with parameter alpha(i), i = 1, 2. Future observations are discounted: at stage m, the payoff is a(m) times the observation Z(m) at that stage. The discount sequence A(n) = (a(1),a(2),...,a(n)...
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作者：ARCONES, MA; CHEN, ZQ; GINE, E
作者单位：William Paterson University New Jersey; University of Connecticut; University of Connecticut
摘要：If a criterion function g(x(1),...,x(m); theta) depends on m > 1 samples, then a natural estimator of arg max P(m)g(x(1),...,x(m); theta) is the arg max of a U-process. It is observed that, under suitable conditions, these estimators are asymptotically normal. This is then applied to prove asymptotic normality of Liu's simplicial median and of Oja's medians in R(d).
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作者：HU, XM; WRIGHT, FT
作者单位：University of Missouri System; University of Missouri Columbia
摘要：Anderson studied the monotonicity of the integral of a symmetric, unimodal density over translates of a symmetric convex set. Restricting attention to elliptically contoured, unimodal densities, Mukerjee, Robertson and Wright weakened the assumption of symmetry on the set and obtained monotonicity properties of power functions, including unbiasedness, for some likelihood ratio tests in order restricted inference for the variance-known case. For elliptically contoured, unimodal densities, we we...
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作者：RUPPERT, D; WAND, MP
作者单位：University of New South Wales Sydney
摘要：Nonparametric regression using locally weighted least squares was first discussed by Stone and by Cleveland. Recently, it was shown by Fan and by Fan and Gijbels that the local linear kernel-weighted least squares regression estimator has asymptotic properties making it superior, in certain senses, to the Nadaraya-Watson and Gasser-Muller kernel estimators. In this paper we extend their results on asymptotic bias and variance to the case of multivariate predictor variables. We are able to deri...
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作者：PITTS, SM
摘要：The GI/G/1 queueing model is regarded as a functional that maps the service and interarrival time distribution functions onto the stationary waiting time distribution function. By considering the output of the functional when it is applied to nonparametric estimators of the input distribution functions, we obtain a nonparametric estimator of the stationary waiting: time distribution function. Using appropriate continuity and differentiability properties of the functional, we show that statisti...
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作者：KNEIP, A
摘要：The paper is concerned with data from a collection of different, but related, regression curves (m(j))(j = 1,...,N), N much greater than 1. In statistical practice, analysis of such data is most frequently based on low-dimensional linear models. It is then assumed that each regression curve mj is a linear combination of a small number L much less than N of common functions g(1),...,g(L). For example, if all m(j)'s are straight lines, this holds with L = 2, g(1) = 1 and g(2)(x) = x. In this pap...
