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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：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：NAIMAN, DQ; WYNN, HP
作者单位：City St Georges, University of London
摘要：Improvements to the classical inclusion-exclusion identity are developed. There are two main results: an abstract combinatoric result and a concrete geometric result. In the abstract result conditions are given which guarantee the existence of a depth d + 1 identity or inequality for the indicator function of a union of a finite collection of events, that is, an expression which is a linear combination of indicator functions of at most (d + 1)-fold intersections of the events. Such an identity...
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作者：HEDAYAT, A
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作者：KUROTSCHKA, V; MULLER, C
摘要：P. J. Bickel's approach to and results on estimating the parameter vector beta of a conditionally contaminated linear regression model by asymptotically linear (AL) estimators beta* which have minimum trace of the asymptotic covariance matrix among all AL estimators with a given bound b on their asymptotic bias (MT-AL estimators with bias bound b) is here extended to conditionally contaminated general linear models and in particular for estimating arbitrary linear aspects phi(beta) = C-beta of...
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作者：OEHLERT, GW
摘要：Ordinary smoothing splines have an integrated mean squared error which is dominated by bias contributions at the boundaries. When the estimated function has additional derivatives, the boundary contribution to the bias affects the asymptotic rate of convergence unless the derivatives of the estimated function meet the natural boundary conditions. This paper introduces relaxed boundary smoothing splines and shows that they obtain the optimal asymptotic rate of convergence without conditions on ...
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作者：PERES, Y
作者单位：Hebrew University of Jerusalem
摘要：Given a sequence of independent, identically distributed random biased bits, von Neumann's simple procedure extracts independent unbiased bits. In this note we show that the number of unbiased bits produced by iterating this procedure is arbitrarily close to the entropy bound.
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作者：MASON, DM
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作者：SWEETING, TJ
摘要：Simple conditions on the observed information ensure asymptotic normality of the conditional distributions of the randomly normed score statistic and maximum likelihood estimator given a suitable asymptotically ancillary statistic. In particular, asymptotic normality holds conditional on any asymptotically ancillary statistic asymptotically equivalent to observed information. The results apply to inference from a general stochastic process and are of particular relevance in the case of nonergo...
