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作者：BUHLMANN, P
摘要：We apply the bootstrap for general stationary observations, proposed by Kunsch, to the empirical process for p-dimensional random vectors. It is known that the empirical process in the multivariate case converges weakly to a certain Gaussian process. We show that the bootstrapped empirical process converges weakly to the same Gaussian process almost surely assuming that the block length l for constructing bootstrap replicates satisfies l(n) = O(n(1/2 -epsilon) ), 0 < epsilon < 1/2, and l(n) --...
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作者：NAIKNIMBALKAR, UV; RAJARSHI, MB
摘要：We show that the empirical process of the block-based bootstrap observations from a stationary sequence converges weakly to an appropriate Gaussian process, conditionally in probability and almost surely depending upon the block length. This bootstrap was introduced by Kunsch and later by Liu and Singh. Applications in estimation of the sampling distribution of a compactly differentiable functional are indicated.
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作者：BOSE, S
摘要：Uncertainty in specification of the prior distribution is a common concern with Bayesian analysis. The robust Bayesian approach is to work with a class of prior distributions, which model uncertainty about the prior, instead of a single distribution. One is interested in the range of the posterior expectations of certain parametric functions as the prior varies over the class being considered-if this range is small, the analysis is robust to mis-specification of the prior. Relatively little re...
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作者：SHEN, XT; WONG, WH
作者单位：University of Chicago
摘要：In this paper, we develop a general theory for the convergence rate of sieve estimates, maximum likelihood estimates (MLE's) and related estimates obtained by optimizing certain empirical criteria in general parameter spaces. In many cases, especially when the parameter space is infinite dimensional, maximization over the whole parameter space is undesirable. In such cases, one has to perform maximization over an approximating space (sieve) of the original parameter space and allow the size of...
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作者：GORDON, L; POLLAK, M
作者单位：Hebrew University of Jerusalem
摘要：Suppose that a system in its standard state produces i.i.d. observations whose distribution is symmetric about zero. At an unknown time the system may leave its standard state, and the observations would subsequently be stochastically larger. Subject to a bound on the rate of false alarms, one wants to detect quickly such a departure from the standard state. We present a robust method of detection which is computationally feasible and remarkably efficient. The method is based on the sequential...
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作者：KNEIP, A
摘要：This paper deals with the following approach for estimating the mean mu of an n-dimensional random vector Y: first, a family S of n x n matrices is specified. Then, an element S is an element of S is selected by Mallows C-L, and mu = S.Y. The case is considered that S is an ''ordered linear smoother'' according to some easily interpretable, qualitative conditions. Examples include linear smoothing procedures in nonparametric regression (as, e.g., smoothing splines, minimax spline smoothers and...
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作者：SRIVASTAVA, MS; WU, YH
作者单位：Stanford University
摘要：In this paper, a dynamic sampling plan in the Shiryayev-Roberts procedure is considered. It is shown that a two-rate dynamic sampling plan is optimal in the sense that it minimizes the stationary average delay time (SADT). Analytical results as well as numerical comparisons show that it is significantly superior to the fixed sampling plan. The comparison also shows that it is as powerful as the dynamic sampling procedure of Assaf and Ritov. The generalizations to the fastinitial response and t...
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作者：DETTE, H
作者单位：University of Gottingen
摘要：In the polynomial regression model of degree m is an element of N we consider the problem of determining a design for the identification of the correct degree of the underlying regression. We propose a new optimality criterion which minimizes a weighted p-mean of the variances of the least squares estimators for the coefficients of x(l) in the polynomial regression models of degree l = 1,..., m. The theory of canonical moments is used to determine the optimal designs with respect to the propos...
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作者：OWEN, A
摘要：Randomized orthogonal arrays provide good sets of input points for exploration of computer programs and for Monte Carlo integration. In 1954, Patterson gave a formula for the randomization variance of the sample mean of a function evaluated at the points of an orthogonal array. That formula is incorrect for most of the arrays that are practical for computer experiments. In this paper we correct Patterson's formula. We also remark on a defect, related tb coincidences, in some orthogonal arrays....
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作者：HEILIGERS, B
摘要：Based on a duality between E-optimality for (sub-) parameters in weighted polynomial regression and a nonlinear approximation problem of Chebyshev type, in many cases the optimal approximate designs on nonnegative and nonpositive experimental regions [a, b] are found to be supported by the extrema of the only equioscillating weighted polynomial over this region with leading coefficient 1. A similar result is stated for regression on symmetric regions [-b, b] for certain subparameters, provided...
