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作者：Chen, DC; Huang, P; Cheng, XZ
作者单位：Uniformed Services University of the Health Sciences - USA; Medical University of South Carolina; George Washington University
摘要：The method of stochastic discrimination (SD) introduced by Kleinberg is a new method in statistical pattern recognition. It works by producing many weak classifiers and then combining them to form a strong classifier. However, the strict mathematical assumptions in Kleinberg [The Annals of Statistics 24 (1996) 2319-2349] are rarely met in practice. This paper provides an applicable way to realize the SD algorithm. We recast SD in a probability-space framework and present a concrete statistical...
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作者：Mykland, PA
作者单位：University of Chicago
摘要：The paper shows how to convert statistical prediction sets into worst case hedging strategies for derivative securities. The prediction sets can, in particular, be ones for volatilities and correlations of the underlying securities, and for interest rates. This permits a transfer of statistical conclusions into prices for options and similar financial instruments. A prime feature of our results is that one can construct the trading strategy as if the prediction set had a 100% probability. If, ...
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作者：Li, B; Cook, RD; Chiaromonte, F
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Minnesota System; University of Minnesota Twin Cities
摘要：Consider the regression of a response Y on a vector of quantitative predictors X and a categorical predictor W. In this article we describe a first method for reducing the dimension of X without loss of information on the conditional mean E(Y\X, W) and without requiring a prespecified parametric model. The method, which allows for, but does not require, parametric versions of the subpopulation mean functions E(Y\X, W = w), includes a procedure for inference about the dimension of X after reduc...
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作者：Huang, JHZ
作者单位：University of Pennsylvania
摘要：In this paper we develop a general theory of local asymptotics for least squares estimates over polynomial spline spaces in a regression problem. The polynomial spline spaces we consider include univariate splines, tensor product splines, and bivariate or multivariate splines on triangulations. We establish asymptotic normality of the estimate and study the magnitude of the bias due to spline approximation. The asymptotic normality holds uniformly over the points where the regression function ...
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作者：Koshevoy, GA; Möttönen, J; Oja, H
作者单位：Russian Academy of Sciences; Central Economics & Mathematics Institute RAS; University of Oulu; University of Jyvaskyla
摘要：We introduce a new scatter matrix functional which is a multivariate affine equivariant extension of the mean deviation E(\x - Med(x)\). The estimate is constructed using the data vectors (centered with the multivariate Oja median) and their angular distances. The angular distance is based on Randles interdirections. The new estimate is called the zonoid covariance matrix (the ZCM), as it is the regular covariance matrix of the centers of the facets of the zonotope based on the data set. There...
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作者：Sasabuchi, S; Tanaka, K; Tsukamoto, T
作者单位：Kyushu University; Hitachi Limited
摘要：Suppose that an order restriction is imposed among several p-variate normal mean vectors. We are interested in testing the homogeneity of these mean vectors under this restriction. This problem is a multivariate extension of Bartholomew's [Biometrika 46 (1959) 36-48]. When the covariance matrices are known, this problem has been studied by Sasabuchi, Inutsuka and Kulatunga [Hiroshima Math. J 22 (1992) 551-560], Sasabuchi, Kulatunga and Saito [Amer. J Math. Management Sci. 18 (1998) 131-158] an...
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作者：Srivastava, MS
作者单位：University of Toronto
摘要：In this article, we consider the case when the number of observations n is less than the dimension p of the random vectors which are assumed to be independent and identically distributed as normal with nonsingular covariance matrix. The central and noncentral distributions of the singular Wishart matrix S = XX', where X is the p x n matrix of observations are derived with respect to Lebesgue measure. Properties of this distribution are given. When the covariance matrix is singular, pseudo sing...
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作者：Zuo, YJ
作者单位：Michigan State University
摘要：A class of projection-based depth functions is introduced and studied. These projection-based depth functions possess desirable properties of statistical depth functions and their sample versions possess strong and order rootn uniform consistency. Depth regions and contours induced from projection-based depth functions are investigated. Structural properties of depth regions and contours and general continuity and convergence results of sample depth regions are obtained. Affine equivariant mul...
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作者：Consonni, G; Veronese, P
作者单位：University of Pavia
摘要：A general Wishart family on a symmetric cone is a natural exponential family (NEF) having a homogeneous quadratic variance function. Using results in the abstract theory of Euclidean Jordan algebras, the structure of conditional reducibility is shown to hold for such a family, and we identify the associated parameterization phi and analyze its properties. The enriched standard conjugate family for phi and the mean parameter mu are defined and discussed. This family is considerably more flexibl...
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作者：Candès, EJ
作者单位：Stanford University
摘要：Feedforward neural networks, projection pursuit regression, and more generally, estimation via ridge functions have been proposed as an approach to bypass the curse of dimensionality and are now becoming widely applied to approximation or prediction in applied sciences. To address problems inherent to these methods-ranging from the construction of neural networks to their efficiency and capability-Canes [Appl. Comput. Harmon. Anal. 6 (1999) 197-218] developed a new system that allows the repre...
