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作者：SHERMAN, RP
摘要：Maximal inequalities for degenerate U-processes of order k, k greater-than-or-equal-to 1, are established. The results rest on a moment inequality (due to Bonami) for kth-order forms and on extensions of chaining and symmetrization inequalities from the theory of empirical processes. Rates of uniform convergence are obtained. The maximal inequalities can be used to determine the limiting distribution of estimators that optimize criterion functions having U-process structure. As an application,...
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作者：STONE, CJ; BUJA, A; HASTIE, T
作者单位：Telcordia Technologies; AT&T; Nokia Corporation; Nokia Bell Labs
摘要：Let X1,...,X(M),Y1,...,Y(N) be random variables, and set X = (X1,...,X(M)) and Y = (Y1,...,Y(N)). Let phi be the regression or logistic or Poisson regression function of Y on X (N = 1) or the logarithm of the density function of Y or the conditional density function of Y on X Consider the approximation phi* to phi having a suitably defined form involving a specified sum of functions of at most d of the variables x1,...,X(M), Y1,...,Y(N) and, subject to this form, selected to minimize the mean ...
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作者：DUDLEY, RM
摘要：Many statisticians have adopted compact differentiability since Reeds showed in 1976 that it holds (while Frechet differentiability fails) in the supremum (sup) norm on the real line for the inverse operator and for the composition operator (F,G) bar arrow pointing right F . G with respect to F. However, these operators are Frechet differentiable with respect to p-variation norms, which for p > 2 share the good probabilistic properties of the sup norm, uniformly over all distributions on the l...
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作者：UHLIG, H
摘要：This paper extends the study of Wishart and multivariate beta distributions to the singular case, where the rank is below the dimensionality. The usual conjugacy is extended to this case. A volume element on the space of positive semidefinite m x m matrices of rank n < m is introduced and some transformation properties established. The density function is found for all rank-n Wishart distributions as well as the rank-1 multivariate beta distribution. To do that, the Jacobian for the transforma...
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作者：STUTE, W
摘要：We introduce a general class of conditional U-statistics and present sufficient conditions for their universal consistency in rth mean. It is shown that under mild assumptions on the smoothing parameters, window and k(n)-nearest neighbor estimators are universally consistent. An application to a new nonparametric discrimination problem is also included.
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作者：HUANG, JS; HUANG, WJ
作者单位：National Sun Yat Sen University
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作者：MATHEW, T; KASALA, S
作者单位：University of North Carolina; University of North Carolina Wilmington
摘要：In the multivariate calibration problem using a multivariate linear model, an exact confidence region is constructed. It is shown that the region is always nonempty and is invariant under nonsingular transformations.
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作者：ROBINSON, PM
摘要：We study problems of semiparametric statistical inference connected with long-memory covariance stationary time series, having spectrum which varies regularly at the origin: There is an unknown self-similarity parameter, but elsewhere the spectrum satisfies no parametric or smoothness conditions, it need not be in L(p), for any p > 1, and in some circumstances the slowly varying factor can be of unknown form. The basic statistic of interest is the discretely averaged periodogram, based on a de...
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作者：QIN, J; LAWLESS, J
摘要：For some time, so-called empirical likelihoods have been used heuristically for purposes of nonparametric estimation. Owen showed that empirical likelihood ratio statistics for various parameters theta(F) of an unknown distribution F have limiting chi-square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parameteric likelihoods. Our objective in this paper is twofold: first, to link estimating functions or equations...
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作者：ZHANG, HP
作者单位：University of Virginia
摘要：A unified approach to deriving confidence regions in linear functional relationship models is presented, based on the conditional likelihood ratio method of Knowles, Siegmund and Zhang. In the case of a single latent predictor, the confidence region for the slope produced by this approach is the familiar one of Fieller and Creasy. However, here it is shown how to derive a confidence region for the slope, when it is known that the slope is positive, that improves on merely intersecting the regi...
