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作者：Jiang, Jiming; Li, Cong; Paul, Debashis; Yang, Can; Zhao, Hongyu
作者单位：University of California System; University of California Davis; Takeda Pharmaceutical Company Ltd; Takeda Pharmaceuticals International, Inc.; Hong Kong Baptist University; Yale University
摘要：We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent genome-wide association studies. The asymptotic analysis establishes consistency of the REML estimator of the variance of the errors in the LMM, and convergence in probability of the REML estimator of the variance of the random effects in the LMM to a certain limit, which is equal to the true variance of the random effects multiplied b...
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作者：Carlier, Guillaume; Chernozhukov, Victor; Galichon, Alfred
作者单位：Universite PSL; Universite Paris-Dauphine; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); New York University; New York University
摘要：We propose a notion of conditional vector quantile function and a vector quantile regression. A conditional vector quantile function (CVQF) of a random vector Y, taking values in R-d given covariates Z = z, taking values in R-k, is a map u bar right arrow Q(Y vertical bar Z) (u, z), which is monotone, in the sense of being a gradient of a convex function, and such that given that vector U follows a reference non-atomic distribution F-U, for instance uniform distribution on a unit cube in Rd, t...
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作者：Lee, Jason D.; Sun, Dennis L.; Sun, Yuekai; Taylor, Jonathan E.
作者单位：University of California System; University of California Berkeley; California State University System; California Polytechnic State University San Luis Obispo; University of California System; University of California Berkeley; Stanford University
摘要：We develop a general approach to valid inference after model selection. At the core of our framework is a result that characterizes. the distribution of a post-selection estimator conditioned on the selection event. We specialize the approach to model selection by the lasso to form valid confidence intervals for the selected coefficients and test whether all relevant variables have been included in the model.
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作者：Qiao, Wanli; Polonik, Wolfgang
作者单位：University of California System; University of California Davis
摘要：This paper provides a rigorous study of the nonparametric estimation of filaments or ridge lines of a probability density f. Points on the filament are considered as local extrema of the density when traversing the support of f along the integral curve driven by the vector field of second eigenvectors of the Hessian of f. We parametrize points on the filaments by such integral curves, and thus both the estimation of integral curves and of filaments will be considered via a plug-in method using...
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作者：Su, Weijie; Candes, Emmanuel
作者单位：Stanford University; Stanford University
摘要：We consider high-dimensional sparse regression problems in which we observe y = X beta + z, where X is an n x p design matrix and z is an n dimensional vector of independent Gaussian errors, each with variance sigma(2). Our focus is on the recently introduced SLOPE estimator [Ann. Appi. Stat. 9 (2015) 1103-1140], which regularizes the least-squares estimates with the rank-dependent penalty Sigma(1 <= i <= p) lambda(i)vertical bar(beta) over cap vertical bar((i)), where vertical bar(beta) over ...
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作者：Ho, Nhat; Nguyen, Xuanlong
作者单位：University of Michigan System; University of Michigan
摘要：We establish minimax lower bounds and maximum likelihood convergence rates of parameter estimation for mean-covariance multivariate Gaussian mixtures, shape-rate Gamma mixtures and some variants of finite mixture models, including the setting where the number of mixing components is bounded but unknown. These models belong to what we call weakly identifiable classes, which exhibit specific interactions among mixing parameters driven by the algebraic structures of the class of kernel densities ...
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作者：Gadat, Sebastien; Klein, Thierry; Marteau, Clement
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：Given an n-sample of random vectors (X-i, Y-i)(1 <= i <= n) whose joint law is unknown, the long-standing problem of supervised classification aims to optimally predict the label Y of a given new observation X. In this context, the k-nearest neighbor rule is a popular flexible and intuitive method in non parametric situations. Even if this algorithm is commonly used in the machine learning and statistics communities, less is known about its prediction ability in general finite dimensional spac...
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作者：Yan, Ting; Leng, Chenlei; Zhu, Ji
作者单位：Central China Normal University; University of Warwick; University of Michigan System; University of Michigan
摘要：Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we provide for the first time a rigorous analysis of directed exponential random graph models using the in-degrees and out-degrees as sufficient statistics with binary as well as continuous weighted edges. We establish the uniform consistency and the asymptotic norma...
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作者：Chang, Jinyuan; Shao, Qi-Man; Zhou, Wen-Xin
作者单位：Southwestern University of Finance & Economics - China; University of Melbourne; Chinese University of Hong Kong; Princeton University
摘要：Two-sample U-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cramer-type moderate deviation theorems for Studentized two-sample U-statistics in a general framework, including the two-sample t-statistic and Studentized Mann Whitney test statistic as prototypical examples. In particular, a refined moderate deviation theorem with second-order accuracy is established for the two-sample t...
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作者：Pillai, Natesh S.; Meng, Xiao-Li
作者单位：Harvard University
摘要：The Cauchy distribution is usually presented as a mathematical curiosity, an exception to the Law of Large Numbers, or even as an Evil distribution in some introductory courses. It therefore surprised us when Drton and Xiao [Bernoulli 22 (2016) 38-59] proved the following result for m = 2 and conjectured it for m >= 3. Let X = (X-1,...,X-m) and Y = (Y-1 ,...,Y-m) be i.i.d. N(0, Sigma), where Sigma = {sigma(ij)} >= 0 is an m x m and arbitrary covariance matrix with sigma(jj) > 0 for all 1 <= j ...
