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作者：JIN, K
作者单位：State University System of Florida; Florida State University
摘要：We provide a solution to the smoothing parameter selection problem involved in the construction of adaptive estimates for the symmetric location model and the general linear model. Linear B-splines are used to give a simple form of the estimate of the score function of the underlying density. New empirical methods are proposed to locate the knots optimally and to select the number of knots. We also give asymptotic bounds for the empirical selection method and show that an estimate with an empi...
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作者：DEVROYE, L
摘要：We consider the Akaike-Parzen-Rosenblatt density estimate f(nh) based upon any superkernel L (i.e., an absolutely integrable function with integral L = 1, whose characteristic function is 1 on [-1, 1]), and compare it with a kernel estimate g(nh) based upon an arbitrary kernel K. We show that for a given subclass of analytic densities, [GRAPHICS] where h > 0 is the smoothing factor. Thus, asymptotically, the class of superkernels is as good as any other class of kernels when certain analytic d...
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作者：LEONARD, T; HSU, JSJ
作者单位：University of California System; University of California Santa Barbara
摘要：A flexible class of prior distributions is proposed, for the covariance matrix of a multivariate normal distribution, yielding much more general hierarchical and empirical Bayes smoothing and inference, when compared with a conjugate analysis involving an inverted Wishart distribution. A likelihood approximation is obtained for the matrix logarithm of the covariance matrix, via Bellman's iterative solution to a Volterra integral equation. Exact and approximate Bayesian, empirical and hierarchi...
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作者：SAMARANAYAKE, K
摘要：The k-armed bandit problem on the Bernoulli dependent arms is discussed. Order relations on the prior distributions of the Bernoulli parameters using moments of the posterior are used to prove a monotonicity property of the value function. When k = 2, a stay-with-a-winner rule is derived for negatively correlated arms and for a certain class of positively correlated arms. These results are extensions of those given in Berry and Fristedt for independent Bernoulli arms. They also generalize the ...
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作者：WASSERMAN, L; KADANE, JB
摘要：As a first step toward developing statistical models based on upper and lower probabilities, we study upper probabilities and upper expectations on the unit interval that are symmetric, by which we mean invariant with respect to equimeasurability. These upper probabilities are generalizations of uniform probability measures. We give some characterizations of these upper probabilities. Specifically, we show that symmetry of the upper expectation functional is equivalent to the underlying set of...
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作者：ZAMAR, RH
摘要：Orthogonal regression M-estimates are considered from a bias robust point of view. Their maximum bias over epsilon-contamination neighborhoods is characterized, and maximum bias curves are computed. The most bias robust orthogonal regression M-estimate is derived and shown to be a ''mode type'' estimate; for instance, in the two-dimensional case this estimate can be computed by locating a strip of fixed width covering the maximum number of data points. It will be shown that, although orthogona...
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作者：DAVIES, L
摘要：Rousseeuw's minimum volume estimator for multivariate location and dispersion parameters has the highest possible breakdown point for an affine equivariant estimator. In this paper we establish that it satisfies a local Holder condition of order 1/2 and converges weakly at the rate of n-1/3 to a non-Gaussian distribution.
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作者：EUBANK, RL; LARICCIA, VN
作者单位：University of Delaware
摘要：Two new statistics for testing goodness-of-fit are derived from the viewpoint of nonparametric density estimation. These statistics are closely related to the Neyman smooth and Cramer-von Mises statistics but are shown to have superior properties both through asymptotic and small sample analyses. Comparison of the proposed tests with the Cramer-von Mises statistic requires the development of a novel technique for comparing tests that are capable of detecting local alternatives converging to th...
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作者：LEHMANN, EL; ROJO, J
作者单位：University of Texas System; University of Texas El Paso
摘要：Statistical concepts of order permeate the theory and practice of statistics. The present paper is concerned with a large class of directional orderings of univariate distributions. (What do we mean by saying that a random variable Y is larger than another random variable X?) Attention is restricted to preorders that are invariant under monotone transformations; this includes orderings such as monotone likelihood ratio, hazard ordering, and stochastic ordering. Simple characterizations of thes...
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作者：VELLAISAMY, P
摘要：Let X1, X2,..., X(k) be k independent gamma random variables with different scale parameters but with a common known shape parameter. Suppose the population corresponding to the largest X(1) [or the smallest X(k)] observation is selected. The problem of estimating the scale parameter theta(1) [or theta(k)] of the selected population is considered. We derive, using the method of differential inequalities, explicit estimators that dominate the natural or the existing estimators. The improved est...
