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作者：Lauritzen, Steffen; Uhler, Caroline; Zwiernik, Piotr
作者单位：University of Copenhagen; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Pompeu Fabra University
摘要：We study exponential families of distributions that are multivariate totally positive of order 2 (MTP2), show that these are convex exponential families and derive conditions for existence of the MLE. Quadratic exponential familes of MTP2 distributions contain attractive Gaussian graphical models and ferromagnetic Ising models as special examples. We show that these are defined by intersecting the space of canonical parameters with a polyhedral cone whose faces correspond to conditional indepe...
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作者：Belitser, Eduard; Ghosal, Subhashis; van Zanten, Harry
作者单位：Vrije Universiteit Amsterdam; North Carolina State University
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作者：Petersen, Alexander; Liu, Xi; Divani, Afshin A.
作者单位：University of California System; University of California Santa Barbara; University of New Mexico
摘要：Data consisting of samples of probability density functions are increasingly prevalent, necessitating the development of methodologies for their analysis that respect the inherent nonlinearities associated with densities. In many applications, density curves appear as functional response objects in a regression model with vector predictors. For such models, inference is key to understand the importance of density-predictor relationships, and the un- certainty associated with the estimated cond...
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作者：Gao, Lan; Fan, Yingying; Lv, Jinchi; Shao, Qi-Man
作者单位：University of Southern California; Southern University of Science & Technology; Chinese University of Hong Kong
摘要：Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null hypothesis of independence between the two random vectors when only the sample size or the dimensionality diverges. Yet its asymptotic null distribution for the more realistic setting when both sample size and dimensionality diverge in the full range remain...
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作者：Kohler, Michael; Langer, Sophie
作者单位：Technical University of Darmstadt
摘要：Recent results in nonparametric regression show that deep learning, that is, neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold. One key feature of the neural networks used in these results is that their network architecture has a further constraint, namely the network sparsity. In this paper, we show that we can get similar results also for least squa...
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作者：Li, Zeng; Wang, Qinwen; Li, Runze
作者单位：Southern University of Science & Technology; Fudan University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. The statistical setting in this paper covers a wide range of highly skewed and heavy-tailed distributions since we do not require the components to be identically distributed, and do not need any moment conditions. We establish the central limit theorem (CLT) for the linear spectral statistics (LSS) of the Kendall...
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作者：Xu, Min; Samworth, Richard J.
作者单位：Rutgers University System; Rutgers University New Brunswick; University of Cambridge
摘要：We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on R-p and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and can mitigate the curse of dimensionality. Our main symmetry assumption is that the super-level sets of the density are K-homothetic (i.e., scalar multiples of a convex body K subset of R-p). When K is known, we prove that the K-homothetic log-concave maximum likelihood...
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作者：Fissler, Tobias; Ziegel, Johanna F.
作者单位：Vienna University of Economics & Business; University of Bern
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作者：Castillo, Ismael; Rockova, Veronika
作者单位：Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; University of Chicago
摘要：This work affords new insights into Bayesian CART in the context of structured wavelet shrinkage. The main thrust is to develop a formal inferential framework for Bayesian tree-based regression. We reframe Bayesian CART as a g-type prior which departs from the typical wavelet product priors by harnessing correlation induced by the tree topology. The practically used Bayesian CART priors are shown to attain adaptive near rate-minimax posterior concentration in the supremum norm in regression mo...
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作者：Chen, Yuxin; Fan, Jianqing; Ma, Cong; Yan, Yuling
作者单位：Princeton University; Princeton University; University of Chicago
摘要：This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers and (3) missing data. This problem, often dubbed as robust principal component analysis (robust PCA), finds applications in various domains. Despite the wide applicability of convex relaxation, the available statistical support (particularly the stability analysis in the presence of random noise) remains highly sub...
