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作者：GITTINS, J; WANG, YG
摘要：For a multiarmed bandit problem with exponential discounting the optimal allocation rule is defined by a dynamic allocation index defined for each arm on its space. The index for an arm is equal to the expected immediate reward from the arm, with an upward adjustment reflecting any uncertainty about the prospects of obtaining rewards from the arm, and the possibilities of resolving those uncertainties by selecting that arm. Thus the learning component of the index is defined to be the differen...
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作者：DONOHO, DL; LOW, MG
作者单位：University of Pennsylvania
摘要：Simple renormalization arguments can often be used to calculate optimal rates of convergence for estimating linear functionals from indirect measurements contaminated with white noise. This allows one to quickly identify optimal rates for certain problems of density estimation, nonparametric regression, signal recovery and tomography. Optimal kernels may also be derived from renormalization; we give examples for deconvolution and tomography.
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作者：JONES, LK
作者单位：University of Massachusetts System; University of Massachusetts Lowell
摘要：A general convergence criterion for certain iterative sequences in Hilbert space is presented. For an important subclass of these sequences, estimates of the rate of convergence are given. Under very mild assumptions these results establish an O(1/ square-root n) nonsampling convergence rate for projection pursuit regression and neural network training; where n represents the number of ridge functions, neurons or coefficients in a greedy basis expansion.
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作者：LIU, RY; SINGH, K
摘要：It is known that the standard delete-1 jackknife and the classical bootstrap are in general equally efficient for estimating the mean-square-error of a statistic in the i.i.d. setting. However, this equivalence no longer holds in the linear regression model. It turns out that the bootstrap is more efficient when error variables are homogeneous and the jackknife is more robust when they are heterogeneous. In fact, we can divide all the commonly used resampling procedures for linear regression m...
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作者：MUKERJEE, H
摘要：The Robbins-Monro process X(n + 1) = X(n) - c(n)Y(n) is a standard stochastic approximation method for estimating the root theta of an unknown regression function. There is a vast literature on the convergence properties of X(n) to theta. In practice, one is also interested in the conditional distribution of the system under the sequential control when the control is set at theta or near theta. This problem appears to have received no attention in the literature. We introduce an estimator usin...
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作者：HALL, P
作者单位：University of Glasgow
摘要：Several authors have developed bootstrap methods for constructing confidence intervals in nonparametric regression. On each occasion a nonpivotal approach has been employed. Nonpivotal methods are still the overwhelmingly popular choice when statisticians use the bootstrap to compute confidence intervals, but they are not necessarily the most appropriate. In this paper we point out some of the theoretical advantages of pivoting. They include a reduction in the error of the bootstrap distributi...
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作者：DETTE, H
摘要：In the class of polynomials of odd (or even) degree up to the order 2r - 1 (2r) optimal designs are determined which minimize a product of the variances of the estimates for the highest coefficients weighted with a prior gamma = (gamma(1),..., gamma(r)), where the numbers gamma(j) correspond to the models of degree 2j - 1 (2j) for j = 1,...,r. For a special class of priors, optimal designs of a very simple structure are calculated generalizing the D1-optimal design for polynomial regression of...
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作者：BARINGHAUS, L; HENZE, N
作者单位：Helmholtz Association; Karlsruhe Institute of Technology
摘要：We study the asymptotic behavior of Mardia's measure of (sample) multivariate skewness. In the special case of an elliptically symmetric distribution, the limit law is a weighted sum of two independent chi2-variates. A normal limit distribution arises if the population distribution has positive skewness. These results explain some curiosities in the power performance of a commonly proposed test for multivariate normality bared on multivariate skewness.
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作者：HE, XM; PORTNOY, S
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：The problem of combining high efficiency with high breakdown properties for regression estimators has piqued the interest of statisticians for some time. One proposal specifically suggested by Rousseeuw and Leroy is to use the least median of squares estimator, omit observations whose residuals are larger than some constant cut-off value and apply least squares to the remaining observations. Although this proposal does retain high breakdown point, it actually converges no faster than the initi...
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作者：SEVERINI, TA; WONG, WH
作者单位：University of Chicago
摘要：In this paper, we outline a general approach to estimating the parametric component of a semiparametric model. For the case of a scalar parametric component, the method is based on the idea of first estimating a one-dimensional subproblem of the original problem that is least favorable in the sense of Stein. The likelihood function for the scalar parameter along this estimated subproblem may be viewed as a generalization of the profile likelihood for that parameter. The scalar parameter is the...
