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作者：CHIU, ST
摘要：The problem of automatic bandwidth selection for a kernel density estimator is considered. It is well recognized that the bandwidth estimate selected by the least squares cross-validation is subject to large sample variation. This difficulty limits the application of the cross-validation estimate. Based on characteristic functions, an important expression for the cross-validation bandwidth estimate is obtained. The expression clearly points out the source of variation. To stabilize the variati...
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作者：PORTNOY, S
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作者：ZAMAN, A
摘要：Suppose X(i) are i.i.d. random variables taking values in X, THETA is a parameter space and y: X x THETA --> R is a map. Define the averages S(n)(y, theta) = (1/n)SIGMA(i = 1)(n)y(X(i), theta) and the truncated expectations T(m)(y, theta) = E max(y(X1, theta), - m). Under the hypothesis of global dominance [i.e., E sup(THETA) y(X1, theta) < infinity] and some regularity conditions, the main result of the paper characterizes the asymptotic suprema of S(n) as follows. For any subset G of THETA, ...
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作者：FELDMAN, I
摘要：In this paper we shall discuss the estimation of the mean of a normal distribution with variance 1. The main question in this work is the existence and computation of a least favorable distribution among all the prior distributions satisfying a given set of constraints. In the following we show that if this distribution is bounded from above on some even moment, then the least favorable distribution exists and it is either normal or discrete. The support of the discrete distribution function d...
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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：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：ELKRUNZ, SM; STUDDEN, WJ
作者单位：Purdue University System; Purdue University
摘要：A Bayesian version of Elfving's theorem is given for the c-optimality criterion with emphasis on the inherent geometry. Conditions under which a one-point design is Bayesian c-optimum are described. The class of prior precision matrices R for which the Bayesian c-optimal designs are supported by the points of the classical c-optimal design is characterized. It is proved that the Bayesian c-optimal design, for large n, is always supported by the same support points as the classical one if the n...
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作者：CSISZAR, I
摘要：An attempt is made to determine the logically consistent rules for selecting a vector from any feasible set defined by linear constraints, when either all n-vectors or those with positive components or the probability vectors are permissible. Some basic postulates are satisfied if and only if the selection rule is to minimize a certain function which, if a prior guess is available, is a measure of distance from the prior guess. Two further natural postulates restrict the permissible distances ...
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作者：HECKMAN, NE; WOODROOFE, M
作者单位：University of Michigan System; University of Michigan
摘要：One observes n data points, (t(i), Y(i)), with the mean of Y(i), conditional on the regression function f, equal to f(t(i)). The prior distribution of the vector f = (f(t1),..., f(t(n)))t is unknown, but ties in a known class-OMEGA. An estimator, f, of f is found which minimizes the maximum E parallel-to f - f parallel-to 2. The maximum is taken over all priors in OMEGA and the minimum is taken over linear estimators of f. Asymptotic properties of the estimator are studied in the case that t(i...
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作者：OWEN, A
摘要：Empirical likelihood is a nonparametric method of inference. It has sampling properties similar to the bootstrap, but where the bootstrap uses resampling, it profiles a multinomial likelihood supported on the sample, Its properties in i.i.d. settings have been investigated in works by Owen, by Hall and by DiCiccio, Hall and Romano. This article extends the method to regression problems. Fixed and random regressors are considered, as are robust and heteroscedastic regressions. To make the exten...
