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作者：Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
作者单位：Northeast Normal University - China; Northeast Normal University - China; University of Hong Kong
摘要：Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLTs) for linear spectral statistics of high-dimensional noncentralized sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for noncentralized sample covariance matrices, some of which even assume Gaussian-like moment conditions. In ...
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作者：Kubjas, Kaie; Robeva, Elina; Sturmfels, Bernd
作者单位：Aalto University; University of California System; University of California Berkeley
摘要：Mixtures of r independent distributions for two discrete random variables can be represented by matrices of nonnegative rank r. Likelihood inference for the model of such joint distributions leads to problems in real algebraic geometry that are addressed here for the first time. We characterize the set of fixed points of the Expectation-Maximization algorithm, and we study the boundary of the space of matrices with nonnegative rank at most 3. Both of these sets correspond to algebraic varietie...
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作者：Loh, Wei-Liem
作者单位：National University of Singapore
摘要：This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of the corresponding fixed-domain asymptotic theory. In particular, we consider: (i) higher-order quadratic variations using nonequispaced line transect data, (ii) second-order quadratic variations from a sample of Gaussian random field observations taken along a...
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作者：Ma, Zongming; Wu, Yihong
作者单位：University of Pennsylvania; University of Illinois System; University of Illinois Urbana-Champaign
摘要：This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. To investigate the tradeoff between statistical performance and computational cost from a complexity-theoretic perspective, we consider a sequence of discretized models which are asymptotically equivalent to the Gaussian model. Under the hypothesis that the planted clique detection problem cannot be solved in randomized polynomial time when the clique size i...
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作者：Zhang, Ting; Wu, Wei Biao
作者单位：Boston University; University of Chicago
摘要：This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this general class of models, an important issue in practice is to address the necessity of modeling the regression function as nonlinear and time-varying. To tackle this, we propose an information criterion and prove its selection consistency property. The results a...
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作者：Amonenk, Inga S.; Robinson, John
作者单位：University of Sydney
摘要：We introduce a nonparametric test statistic for the permutation test in complete block designs. We find the region in which the statistic exists and consider particularly its properties on the boundary of the region. Further, we prove that saddlepoint approximations for tail probabilities can be obtained inside the interior of this region. Finally, numerical examples are given showing that both accuracy and power of the new statistic improves on these properties of the classical F-statistic un...
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作者：Jiang, Fei; Ma, Yanyuan; Wang, Yuanjia
作者单位：Harvard University; University of South Carolina System; University of South Carolina Columbia; Columbia University
摘要：We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and modify the generalized estimating equation to facilitate estimation and inference. We use local smoothing kernel to estimate the unspecified coefficient functions of time, and use B-splines to estimate the unspecified function of the single index component. The ...
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作者：Can, Sami Umut; Einmahl, John H. J.; Khmaladze, Estate V.; Laeven, Roger J. A.
作者单位：University of Amsterdam; Tilburg University; Victoria University Wellington
摘要：Let (X-1, Y-1),..., (X-n, Y-n) be an i.i.d sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima V-i=1(n) X-i and V-i=1(n) Y-i is then characterized by the marginal extreme value indices and the tail copula R. We propose a procedure for constructing asymptotically distribution-free goodness-of-fit tests for the tail copula R. The procedure is based on ...
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作者：Zheng, Wei
作者单位：Purdue University System; Purdue University; Purdue University in Indianapolis
摘要：A systematic study is carried out regarding universally optimal designs under the interference model, previously investigated by Kunert and Martin [Ann. Statist. 28 (2000) 1728-1742] and Kunert and Mersmann [J. Statist. Plann. Inference 141 (2011) 1623-1632]. Parallel results are also provided for the undirectional interference model, where the left and right neighbor effects are equal. It is further shown that the efficiency of any design under the latter model is at least its efficiency unde...
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作者：Giraud, Christophe; Roueff, Francois; Sanchez-Perez, Andres
作者单位：Universite Paris Saclay; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS)
摘要：In this work, we study the problem of aggregating a finite number of predictors for nonstationary sub-linear processes. We provide oracle inequalities relying essentially on three ingredients: (1) a uniform bound of the 1 norm of the time varying sub-linear coefficients, (2) a Lipschitz assumption on the predictors and (3) moment conditions on the noise appearing in the linear representation. Two kinds of aggregations are considered giving rise to different moment conditions on the noise and m...
