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作者：Diaconis, P; Sturmfels, B
作者单位：Cornell University; University of California System; University of California Berkeley
摘要：We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include contingency tables, logistic regression, and spectral analysis of permutation data. The algorithms involve computations in polynomial rings using Grobner bases.
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作者：Girard, DA
作者单位：Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：When using nonparametric estimates of the mean curve, surface or image underlying noisy observations, the selection of smoothing parameters is generally crucial. This paper gives a theoretical comparison of the performances of generalized cross-validation (GCV) and of its fast randomized version (RGCV), as selection criteria. This is mainly done by studying the asymptotic distribution of the excess error for each selector, that is, the difference between the (data-driven) resulting average squ...
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作者：Mallat, S; Papanicolaou, G; Zhang, ZF
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Stanford University
摘要：It is shown that the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions. We model locally stationary processes with pseudo-differential operators that are time-varying convolutions. An adaptive covariance estimation is calculated by searching first for a best local cosine basis which approximates the covariance by a band or a diagonal matrix. The estimation is obtained from regularized versions of the diagonal coefficients in the be...
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作者：Müller-Gronbach, T; Ritter, K
作者单位：Free University of Berlin; University of Passau
摘要：We study integration and reconstruction of Gaussian random functions with inhomogeneous local smoothness. A single realization may only be observed at a finite sampling design and the correct local smoothness is unknown. We construct adaptive two-stage designs that lead to asymptotically optimal methods. We show that every nonadaptive design is less efficient.
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作者：Luo, Z
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：A computational scheme for fitting smoothing spline ANOVA models to large data sets with a (near) tensor product design is proposed. Such data sets are common in spatial-temporal analyses. The proposed scheme uses the backfitting algorithm to take advantage of the tensor product design to save both computational memory and time. Several ways to further speed up the backfitting algorithm, such as collapsing component functions and successive over-relaxation, are discussed. An iterative imputati...
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作者：Miller, FR; Neill, JW; Sherfey, BW
作者单位：Kansas State University; Kansas State University
摘要：To assess the adequacy of a nonreplicated linear regression model, Christensen introduced the concepts of orthogonal between- and within-cluster lack of fit with corresponding optimal tests. However, the properties of these tests depend on the choice of near-replicate clusters. In this paper, a graph theoretic framework is presented to represent candidate clusterings. A clustering is then selected according to a proposed maximin power criterion from among the clusterings consistent with a spec...
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作者：Spokoiny, VG
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We propose a method of adaptive estimation of a regression function which is near optimal in the classical sense of the mean integrated error. At the same time, the estimator is shown to be very sensitive to discontinuities or change-points of the underlying function f or its derivatives. For instance, in the case of a jump of a regression function, beyond the intervals of length (in order) n(-1) log n around change-points the quality of estimation is essentially the same as if locations of ju...
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作者：He, SY; Yang, GL
作者单位：Peking University; University System of Maryland; University of Maryland College Park
摘要：The random truncation model is defined by the conditional probability distribution H(x, y) = P[X less than or equal to x, Y less than or equal to y\X greater than or equal to Y] where X and Y are independent random variables. A problem of interest is the estimation of the distribution function F of X with data from the distribution H. Under random truncation, F need not be fully identifiable from H and only a part of it, say F-0, is. We show that the nonparametric MLE F-n of F-0 obeys the stro...
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作者：Salinelli, E
作者单位：University of Turin
摘要：Nonlinear principal components for an absolutely continuous random vector X with positive bounded density are defined as the solution of a variational problem in a suitable function space. In this way transformations depending on all the components of X are obtained. Some properties of nonlinear principal components are proved: in particular, it is shown that the set of nonlinear principal transformations of X is an orthonormal basis for the function space associated with the optimal problem. ...
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作者：Cai, TT; Brown, LD
作者单位：Purdue University System; Purdue University; University of Pennsylvania
摘要：Standard wavelet shrinkage procedures for nonparametric regression are restricted to equispaced samples. There, data are transformed into empirical wavelet coefficients and threshold rules are applied to the coefficients. The estimators are obtained via the inverse transform of the denoised wavelet coefficients. In many applications, however, the samples are nonequispaced. It can be shown that these procedures would produce suboptimal estimators if they were applied directly to nonequispaced s...
