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作者：Kennedy, Edward h.; Balakrishnan, Sivaraman; Robins, James m.; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：Estimation of heterogeneous causal effects-that is, how effects of poli-cies and treatments vary across subjects-is a fundamental task in causal in-ference. Many methods for estimating conditional average treatment effects(CATEs) have been proposed in recent years, but questions surrounding op-timality have remained largely unanswered. In particular, a minimax theoryof optimality has yet to be developed, with the minimax rate of convergenceand construction of rate-optimal estimators remaining ...
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作者：Yan, Yuling; Chen, Yuxin; Fan, Jianqing
作者单位：Massachusetts Institute of Technology (MIT); University of Pennsylvania; Princeton University
摘要：This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly underexplored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in general difficult in high dimension, the challenge is further compounded by the prevalent presence of missing data and heteroskedastic noise. We propose a novel approach to performing valid inference on the principal subspace, on the basis of an estimator ca...
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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 ...
