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作者：LU, IL; RICHARDS, D
作者单位：University of Virginia
摘要：Let X1, X2,...,X(n) be a random sample from a continuous univariate distribution F, and let DELTA = PI 1 less-than-or-equal-to i < j less-than-or-equal-to n(X(i) - X(j))2 denote the t, or square of the Vandermonde determinant, constructed from the random sample. The statistic DELTA arises in the study of moment matrices and inference for mixture distributions, the spectral theory of random matrices, control theory and statistical physics. In this paper, we study the probability distribution of...
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作者：BUTLER, RW; DAVIES, PL; JHUN, M
作者单位：University of Duisburg Essen; Korea University
摘要：Consistency is shown for the minimum covariance determinant (MCD) estimators of multivariate location and scale and asymptotic normality is shown for the former. The proofs are made possible by showing a separating ellipsoid property for the MCD subset of observations. An analogous property is shown for the MCD subset computed from the population distribution.
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作者：DETTE, H
摘要：In a recent paper Pukelsheim and Studden determined the E-optimal design for the polynomial regression model on the interval [-1, 1] where the variances of different observations are assumed to be constant. In this note we show that these results can be generalized for polynomial regression models with non constant variances proportional to specific functions.
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作者：MARTIN, RD; ZAMAR, RH
作者单位：University of British Columbia
摘要：In this paper we consider the problem of robust estimation of the scale of the location residuals when the underlying distribution of the data belongs to a contamination neighborhood of a parametric location-scale family. We define the class of M-estimates of scale with general location, and show that under certain regularity assumptions, these scale estimates converge to their asymptotic functionals uniformly with respect to the underlying distribution, and with respect to the M-estimate defi...
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作者：WU, JS; CHU, CK
作者单位：National Tsing Hua University
摘要：In the fixed-design nonparametric regression model, kernel-type estimators of the locations of jump points and the corresponding sizes of jump values of the regression function are proposed. These kernel-type estimators are analyzed with almost sure results and limiting distributions. Using the limiting distributions, we are able to test the number of jump points and give asymptotic confidence intervals for the sizes of jump values of the regression function. Simulation studies demonstrate tha...
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作者：BJERVE, S; DOKSUM, K
作者单位：University of California System; University of California Berkeley
摘要：For.experiments where the strength of association between a response variable Y and a covariate X is different over different regions of values for the covariate X, we propose local nonparametric dependence functions which measure the strength of association between Y and X as a function of X = x. Our dependence functions are extensions of Galton's idea of strength of co-relation from the bivariate normal case to the nonparametric case. In particular, a dependence function is obtained by expre...
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作者：KHMALADZE, EV
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：This paper is mainly devoted to the following statistical problem: in the case of random variables of any finite dimension and both simple or parametric hypotheses, how to construct convenient ''empirical'' processes which could provide the basis for goodness of fit tests-more or less in the same way as the uniform empirical process does in the case of simple hypothesis and scalar random variables. The solution of this problem is connected here with the theory of multiparameter martingales and...
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作者：KUNSCH, H; BERAN, J; HAMPEL, F
作者单位：University of Zurich; Texas A&M University System; Texas A&M University College Station
摘要：The background of the paper is the empirical observation from a variety of subject areas that long-range correlations appear to be much more frequent than has been previously assumed. This includes high-quality measurement series which are commonly treated as prototypes of ''i.i.d.'' observations. Evidence is briefly cited in the paper. It has already been shown elsewhere that long-range dependence leads to results that can be qualitatively different from those obtained under short-range depen...
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作者：KOUL, HL; SALEH, AKME
作者单位：Carleton University
摘要：In an AR(p) model, R-estimation of a subset of parameters is considered when the complementary subset is possibly redundant. Along with the rank test of the full hypothesis and the subhypothesis of the parameters, both preliminary test and shrinkage R-estimators are considered. In the light of asymptotic distributional risks, the relative asymptotic risk-efficiency results are given. Though, the shrinkage R-estimator may dominate their classical versions, they do not in general dominate the pr...
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作者：OSULLIVAN, F
摘要：Nonparametric estimation of the relative risk in a generalized Cox model with multivariate time dependent covariates is considered. Estimation is based on a penalized partial likelihood. Using techniques from Andersen and Gill, and Cox and O'Sullivan, upper bounds on rate of convergence in a variety of norms are obtained. These upper bounds match the optimal rates available for linear nonparametric regression and density estimation. The results are uniform in the smoothing parameter, which is ...
