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作者：Kalifa, K; Mallat, S
作者单位：Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; New York University
摘要：Thresholding algorithms in an orthonormal basis are studied to estimate noisy discrete signals degraded by a linear operator whose inverse is not bounded. For signals in a set Theta, sufficient conditions are established on the basis to obtain a maximum risk with minimax rates of convergence. Deconvolutions with kernels having a Fourier transform which vanishes at high frequencies are examples of unstable inverse problems, where a thresholding in a wavelet basis is a suboptimal estimator. A ne...
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作者：Zhang, SL; Wong, MY
作者单位：Michigan Technological University; Heilongjiang University; Hong Kong University of Science & Technology
摘要：Additive regression models have turned out to be useful statistical tools in the analysis of high-dimensional data. The attraction of such models is that the additive component can be estimated with the same optimal convergence rate as a one-dimensional nonparametric regression. However, this optimal property holds only when all the additive components have the same degree of homogeneous smoothness. In this paper, we propose a two-step wavelet thresholding estimation process in which the estim...
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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：Pons, O
作者单位：Universite Paris Saclay; INRAE; Universite Paris Cite
摘要：We consider a nonregular Cox model for independent and identically distributed right censored survival times, with a change-point according to the unknown threshold of a covariate. The maximum partial likelihood estimators of the parameters and the estimator of the baseline cumulative hazard are studied. We prove that the estimator of the change-point is n-consistent and the estimator of the regression parameters are n(1/2)-consistent, and we establish the asymptotic distributions of the estim...
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作者：Shafie, K; Sigal, B; Siegmund, D; Worsley, KJ
作者单位：Shahid Beheshti University; Stanford University; Stanford University; McGill University
摘要：Siegmund and Worsley considered the problem of testing for a signal with unknown location and scale in a Gaussian random field defined on RN. The test statistic was the maximum of a Gaussian random field in an (N + 1)-dimensional scale space, N dimensions for location and one dimension for the scale of a smoothing kernel. Siegmund and Worsley used two methods, one involving the expected Euler characteristic of the excursion set and the other involving the volume of tubes, to derive an approxim...
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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：Hössjer, O
作者单位：Stockholm University
摘要：We consider estimation of a disease susceptibility locus tau at a chromosome. With perfect marker data available, the estimator (tau) over cap (N) of r based on N pedigrees has a rate of convergence N-1 under mild regularity conditions. The limiting distribution is the arg max of a certain compound Poisson process. Our approach is conditional on observed phenotypes, and therefore treats parametric and nonparametric linkage, as well as quantitative trait loci methods within a unified framework....
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作者：Hall, P; Molchanov, I
作者单位：Australian National University; University of Bern
摘要：In fault-line estimation in spatial problems it is sometimes possible to choose design points sequentially, by working one's way gradually through the response plane, rather than distributing design points across the plane prior to conducting statistical analysis. For example, when estimating a change line in the concentration of resources on or under the sea bed, individual measurements can be particularly expensive to make. In such cases, sequential, design-adaptive methods are attractive. A...
