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作者：Duan, Yaqi; Wang, Mengdi; Wainwright, Martin j.
作者单位：New York University; Princeton University; Massachusetts Institute of Technology (MIT)
摘要：We study nonparametric methods for estimating the value function of an infinite-horizon discounted Markov reward process (MRP). We analyze the kernel-based least-squares temporal difference (LSTD) estimate, which can be understood either as a nonparametric instrumental variables method, or as a projected approximation to the Bellman fixed point equation. Our analysis imposes no assumptions on the transition operator of the Markov chain, but rather only conditions on the reward function and pop...
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作者：Guan, Leying
作者单位：Yale University
摘要：Permutation tests are widely recognized as robust alternatives to tests based on normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their assumption-free guarantees for controlling type I error in partial correlation tests. To address this ongoing challenge, we have developed a conformal test through permutation-augmented regressions, which we refer to as PALMRT. PALMRT not only achieves power competitive with...
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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：Bao, Zhigang; Hu, Jiang; Xu, Xiaocong; Zhang, Xiaozhuo
作者单位：University of Hong Kong; Northeast Normal University - China; Hong Kong University of Science & Technology
摘要：A fundamental concept in multivariate statistics, the sample correlation matrix, is often used to infer the correlation/dependence structure among random variables, when the population mean and covariance are unknown. A natural block extension of it, the sample block correlation matrix, is proposed to take on the same role, when random variables are generalized to random subvectors. In this paper, we establish a spectral theory of the sample block correlation matrices and apply it to group ind...
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作者：Wang, Yuhao; Shah, Rajen d.
作者单位：Tsinghua University; University of Cambridge
摘要：We consider estimation of average treatment effects given observational data with high-dimensional pretreatment variables. Existing methods for this problem typically assume some form of sparsity for the regression functions. In this work, we introduce a debiased inverse propensity score weighting (DIPW) scheme for average treatment effect estimation that delivers root nconsistent estimates when the propensity score follows a sparse logistic regression model; the outcome regression functions a...
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作者：Yang, Songshan; Zheng, Shurong; Li, Runze
作者单位：Renmin University of China; Renmin University of China; Northeast Normal University - China; Northeast Normal University - China; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：This paper is concerned with high-dimensional two-sample mean problems, which receive considerable attention in recent literature. To utilize the correlation information among variables for enhancing the power of two- sample mean tests, we consider the setting in which the precision matrix of high-dimensional data possesses a linear structure. Thus, we first propose a new precision matrix estimation procedure with considering its linear structure, and further develop regularization methods to ...
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作者：Steinberger, Lukas
作者单位：University of Vienna
摘要：We develop a theory of asymptotic efficiency in regular parametric models when data confidentiality is ensured by local differential privacy (LDP). Even though efficient parameter estimation is a classical and well-studied problem in mathematical statistics, it leads to several nontrivial obstacles that need to be tackled when dealing with the LDP case. Starting from a regular parametric model P = (P theta)theta E Theta, Theta C Rp, for the i.i.d. unobserved sensitive data X 1 , ...,Xn, we est...
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作者：Lei, Jing; Zhang, Anru R.; Zhu, Zihan
作者单位：Carnegie Mellon University; Duke University; University of Pennsylvania
摘要：We study the problem of community recovery and detection in multi- layer stochastic block models, focusing on the critical network density threshold for consistent community structure inference. Using a prototypical two- block model, we reveal a computational barrier for such multilayer stochastic block models that does not exist for its single-layer counterpart: When there are no computational constraints, the density threshold depends linearly on the number of layers. However, when restricte...
