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作者：Zhang, Lu; Lu, Junwei
作者单位：Harvard University; Harvard University
摘要：Variable selection on the large-scale networks has been extensively studied in the literature. While most of the existing methods are limited to the local functionals especially the graph edges, this paper focuses on selecting the discrete hub structures of the networks. Specifically, we propose an inferential method, called StarTrek filter, to select the hub nodes with degrees larger than a certain thresholding level in the high-dimensional graphical models and control the false discovery rat...
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作者：Kley, Tobias; Liu, Yuhan philip; Cao, Hongyuan; Wu, Wei biao
作者单位：University of Gottingen; University of Chicago; State University System of Florida; Florida State University
摘要：This paper considers the problem of testing and estimation of change point where signals after the change point can be highly irregular, which departs from the existing literature that assumes signals after the change point to be piecewise constant or vary smoothly. A two-step approach is proposed to effectively estimate the location of the change point. The first step consists of a preliminary estimation of the change point that allows us to obtain unknown parameters for the second step. In t...
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作者：Oesting, Marco; Wintenberger, Olivier
作者单位：University of Stuttgart; University of Stuttgart; Universite Paris Cite; Sorbonne Universite
摘要：The extremal dependence structure of a regularly varying random vector X is fully described by its limiting spectral measure. In this paper, we investigate how to recover characteristics of the measure, such as extremal coefficients, from the extremal behaviour of convex combinations of components of X. Our considerations result in a class of new estimators of moments of the corresponding combinations for the spectral vector. We show asymptotic normality by means of a functional limit theorem ...
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作者：Dey, Anurag; Chaudhuri, Probal
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：The weak convergence of the quantile processes, which are constructed based on different estimators of the finite population quantiles, is shown under various well-known sampling designs based on a superpopulation model. The results related to the weak convergence of these quantile processes are applied to find asymptotic distributions of the smooth L-estimators and the estimators of smooth functions of finite population quantiles. Based on these asymptotic distributions, confidence intervals ...
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作者：Fan, Jianqing; Fang, Cong; Gu, Yihong; Zhang, Tong
作者单位：Princeton University; Peking University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：This paper considers a multi-environment linear regression model in which data from multiple experimental settings are collected. The joint distribution of the response variable and covariates may vary across different environments, yet the conditional expectations of the response variable, given the unknown set of important variables, are invariant. Such a statistical model is related to the problem of endogeneity, causal inference, and transfer learning. The motivation behind it is illustrat...
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作者：Oliveira, Roberto i.; Rico, Zoraida f.
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Columbia University
摘要：We present an estimator of the covariance matrix Sigma of random ddimensional vector from an i.i.d. sample of size n. Our sole assumption is that this vector satisfies a bounded L-p - L-2 moment assumption over its onedimensional marginals, for some p > 4. Given this, we show that E can be estimated from the sample with the same high-probability error rates that the sample covariance matrix achieves in the case of Gaussian data. This holds even though we allow for very general distributions th...
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作者：Cai, T. tony; Kim, Dongwoo; Pu, Hongming
作者单位：University of Pennsylvania
摘要：This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where in addition to observations from the target distribution, auxiliary samples from similar but distinct source distributions are available. The paper considers both common and independent designs and establishes the minimax rates of convergence for both designs. The results reveal an interesting phase transition phenomenon under the two designs and demonstrate the benefits of ...
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作者：Cai, T. Tony; Chen, Ran; Zhu, Yuancheng
作者单位：University of Pennsylvania
摘要：Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a procedure is evaluated at individual functions. Fully adaptive and computationally efficient algorithms are proposed and sharp minimax lower bounds are given for both the estimation accuracy and expected length of confidence intervals for the minimizer and ...
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作者：Yan, Han; Chen, Song Xi
作者单位：Peking University; Tsinghua University
摘要：Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model for temporally dependent data with segmenting boundaries depending on multivariate covariates with nondiminishing boundary effects. A mixed integer quadratic programming algorithm is formulated to facilitate the least square estimation of the regression and ...
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作者：Davis, Damek; Drusvyatskiy, Dmitriy; Jiang, Liwei
作者单位：Cornell University; University of Washington; University of Washington Seattle
摘要：In their seminal work, Polyak and Juditsky showed that stochastic approximation algorithms for solving smooth equations enjoy a central limit theorem. Moreover, it has since been argued that the asymptotic covariance of the method is best possible among any estimation procedure in a local minimax sense of H & aacute;jek and Le Cam. A long-standing open question in this line of work is whether similar guarantees hold for important nonsmooth problems, such as stochastic nonlinear programming or ...
