-
作者：Bellec, Pierre C.
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：We study the problem of aggregation of estimators when the estimators are not independent of the data used for aggregation and no sample splitting is allowed. If the estimators are deterministic vectors, it is well known that the minimax rate of aggregation is of order log(M), where M is the number of estimators to aggregate. It is proved that for affine estimators, the minimax rate of aggregation is unchanged: it is possible to handle the linear dependence between the affine estimators and th...
-
作者：Leung, Dennis; Drton, Mathias
作者单位：Chinese University of Hong Kong; University of Washington; University of Washington Seattle
摘要：We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank correlations. In the asymptotic regime where both m and n tend to infinity, a martingale central limit theorem is applied to show that the null distributions of these statistics converge to Gaussian limits, which are valid with no specific distributional or m...
-
作者：Perry, Amelia; Wein, Alexander S.; Bandeira, Afonso S.; Moitra, Ankur
作者单位：Massachusetts Institute of Technology (MIT); New York University; New York University; Massachusetts Institute of Technology (MIT)
摘要：A central problem of random matrix theory is to understand the eigen-values of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or spike) is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Peche showed that the spiked Wishart ensemble exhibits a sharp phase transition asymptotically: when the spike strength is above a critical thr...
-
作者：Chen, Yudong; Li, Xiaodong; Xu, Jiaming
作者单位：Cornell University; University of California System; University of California Davis; Purdue University System; Purdue University
摘要：The stochastic block model (SBM), a popular framework for studying community detection in networks, is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees. The degree-corrected stochastic block model (DCSBM) is a natural extension of SBM that allows for degree heterogeneity within communities. To find the communities under DCSBM, this paper proposes a convexified modularity maximization approach, which is based on a convex...
-
作者：Behr, Merle; Holmes, Chris; Munk, Axel
作者单位：University of Gottingen; University of Oxford; Max Planck Society
摘要：We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an epsilon-neighborhood of the mixture when the sources take only values in a known finite alphabet. Based on this we provide the SLAM (Separates Linear Alphabet Mixtures) estimators for the mixing weights and sources. For Gaussian error, we obtain uniform confidence sets and ...
-
作者：Freund, Robert M.; Grigas, Paul; Mazumder, Rahul
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
摘要：We analyze boosting algorithms [Ann. Statist. 29 (2001) 1189-1232; Ann. Statist. 28 (2000) 337-407; Ann. Statist. 32 (2004) 407-499] in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental forward stagewise algorithm (FS epsilon) and least squares boosting [LS-BOOST(epsilon)], can be viewed as subgradient descent to minimize the loss function defined as the maxi...
-
作者：Liu, Weidong
作者单位：Shanghai Jiao Tong University; Shanghai Jiao Tong University
摘要：We present a new framework on inferring structural similarities and differences among multiple high-dimensional Gaussian graphical models (GGMs) corresponding to the same set of variables under distinct experimental conditions. The new framework adopts the partial correlation coefficients to characterize the potential changes of dependency strengths between two variables. A hierarchical method has been further developed to recover edges with different or similar dependency strengths across mul...
-
作者：Ray, Kolyan
作者单位：Leiden University; Leiden University - Excl LUMC
摘要：We investigate Bernstein-von Mises theorems for adaptive nonparametric Bayesian procedures in the canonical Gaussian white noise model. We consider both a Hilbert space and multiscale setting with applications in L-2 and L-infinity, respectively. This provides a theoretical justification for plug-in procedures, for example the use of certain credible sets for sufficiently smooth linear functionals. We use this general approach to construct optimal frequentist confidence sets based on the poste...
-
作者：Lok, Judith J.
作者单位：Harvard University; Harvard T.H. Chan School of Public Health
摘要：In observational studies, treatment may be adapted to covariates at several times without a fixed protocol, in continuous time. Treatment influences covariates, which influence treatment, which influences covariates and so on. Then even time-dependent Cox-models cannot be used to estimate the net treatment effect. Structural nested models have been applied in this setting. Structural nested models are based on counterfactuals: the outcome a person would have had had treatment been withheld aft...
-
作者：Rousseau, Judith; Szabo, Botond
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Budapest University of Technology & Economics; Leiden University - Excl LUMC; Leiden University
摘要：We consider the asymptotic behaviour of the marginal maximum likelihood empirical Bayes,posterior distribution in general setting. First, we characterize the set where the maximum marginal likelihood estimator is located with high probability. Then we provide oracle type of upper and lower bounds for the contraction rates of the empirical Bayes posterior. We also show that the hierarchical Bayes posterior achieves the same contraction rate as the maximum marginal likelihood empirical Bayes pos...
