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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：Hassani, Hamed; Javanmard, Adel
作者单位：University of Pennsylvania; University of Southern California
摘要：Successful deep learning models often involve training neural network architectures that contain more parameters than the number of training samples. Such overparametrized models have recently been extensively studied, and the virtues of overparametrization have been established from both the statistical perspective, via the double-descent phenomenon, and the computational perspective via the structural properties of the optimization landscape. Despite this success, it is also well known that ...
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作者：He, Yong; Kong, Xinbing; Trapani, Lorenzo; Yu, Long
作者单位：Shandong University; Nanjing Audit University; University of Pavia; Shanghai University of Finance & Economics
摘要：This paper proposes a novel methodology for the online detection of changepoints in the factor structure of large matrix time series. Our approach is based on the well-known fact that, in the presence of a changepoint, the number of spiked eigenvalues in the second moment matrix of the data increases (e.g., in the presence of a change in the loadings, or if a new factor emerges). Based on this, we propose two families of procedures-one based on the fluctuations of partial sums, and one based o...
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作者：Agapiou, Sergios; Castillo, Ismael
作者单位：University of Cyprus; Sorbonne Universite; Universite Paris Cite
摘要：We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy-tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior distributions achieve adaptive rates of contraction in the minimax sense (up to logarithmic factors) without the need to sample hyperparameters. Unlike many existing procedures, where a form of direct model (or estimator) selection is performed, the method can be se...
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作者：Chen, Xi; Jing, Wenbo; Liu, Weidong; Zhang, Yichen
作者单位：New York University; Shanghai Jiao Tong University; Purdue University System; Purdue University
摘要：The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semiparametric binary choice model under a distributed computing environment without prespecifying the noise distribution. An intuitive divideand-conquer estimator is computationally expensive and restricted by a nonregular constraint on the number of machines, due to the hig...
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作者：Cattaneo, Matias d.; Chandak, Rajita; Klusowski, Jason m.
作者单位：Princeton University
摘要：We develop a theoretical framework for the analysis of oblique decision trees, where the splits at each decision node occur at linear combinations of the covariates (as opposed to conventional tree constructions that force axisaligned splits involving only a single covariate). While this methodology has garnered significant attention from the computer science and optimization communities since the mid-80s, the advantages they offer over their axisaligned counterparts remain only empirically ju...
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作者：Dubey, Paromita; Chen, Yaqing; Muller, Hans-Georg
作者单位：University of Southern California; Rutgers University System; Rutgers University New Brunswick; University of California System; University of California Davis
摘要：This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain structural conditions and features a probability measure. We refer to the random elements of such spaces as random objects and to the emerging field that deals with their statistical analysis as metric statistics. Metric statistics provides methodology, theory an...
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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...
