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作者：Larsson, Martin; Ramdas, Aaditya; Ruf, Johannes
作者单位：Carnegie Mellon University; Carnegie Mellon University; Carnegie Mellon University; University of London; London School Economics & Political Science
摘要：We consider testing a composite null hypothesis P against a point alternative Q using e-variables, which are nonnegative random variables X such that E-P[X] <= 1 for every P is an element of P. This paper establishes a fundamental result: under no conditions whatsoever on P or Q, there exists a special evariable X* that we call the numeraire, which is strictly positive and satisfies E-Q[X/X*] <= 1 for every other e-variable X. In particular, X* is log-optimal in the sense that E-Q[log(X/X*)] <...
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作者：Hen, Fan; Mei, Song; Bai, Yu
作者单位：Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley; Salesforce
摘要：Modern Reinforcement Learning (RL) is more than just learning the optimal policy; alternative learning goals such as exploring the environment, estimating the underlying model and learning from preference feedback are all of practical importance. While provably sample-efficient algorithms for each specific goal have been proposed, these algorithms often depend strongly on the particular learning goal, and thus admit different structures correspondingly. It is an urging open question whether th...
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作者：Jiang, Jiming
作者单位：University of California System; University of California Davis
摘要：Generalized linear mixed models (GLMM) with crossed random effects is infamously known to present major challenges not only computationally but also theoretically. In fact, to date only consistency of the maximum likelihood estimators (MLE) has been proved for GLMM with crosses random effects. We introduce a new technique in asymptotic analysis built on a second-order Laplace approximation (LA) of a conditional expectation, whose coefficients are carefully evaluated. The LA leads to a large sy...
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作者：Dufour, Jean-Marie; Renault, Eric; Zinde-Walsh, Victoria
作者单位：McGill University; University of Warwick
摘要：This paper provides an exhaustive characterization of the asymptotic null distribution of Wald-type statistics for testing restrictions given by polynomial functions-which may involve singularities-when the limiting distribution of the parameter estimator is absolutely continuous (e.g., Gaussian). In addition to the well-known finite-sample noninvariance, there is also an asymptotic noninvariance (nonpivotality): with standard critical values, the test may either under-reject or over-reject, a...
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作者：Einmahl, John h. j.; Krajina, Andrea; Cai, Juan juan
作者单位：Tilburg University; University of Gottingen; Vrije Universiteit Amsterdam
摘要：Multivariate regular variation is a common assumption in the statistics literature and needs to be verified in real-data applications. We develop a novel hypothesis test for multivariate regular variation, employing localized empirical likelihood. We establish the weak convergence of the test statistic to a nonstandard, distribution-free limit and hence can provide universal critical values for the test. We show the very good finite-sample behavior of the procedure through simulations and appl...
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作者：Divol, Vincent; Niles-Weed, Jonathan; Pooladian, Aram-Alexandre
作者单位：Institut Polytechnique de Paris; ENSAE Paris; New York University; New York University
摘要：We study the problem of estimating a function T, given independent samples from a distribution P and from the pushforward distribution TAP. This setting is motivated by applications in the sciences, where T represents the evolution of a physical system over time, and in machine learning, where, for example, T may represent a transformation learned by a deep neural network trained for a generative modeling task. To ensure identifiability, we assume that T = del phi 0 is the gradient of a convex...
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作者：Van Delft, Anne; Blumberg, Andrew J.
作者单位：Columbia University; Columbia University
摘要：We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric space-valued stochastic process, possibly of nonstationary nature, thereby integrating geometric data analysis into the realm of functional time series analysis. Our framework allows for natural incorporation of spatial-temporal dynamics, heterogeneous sampling, and...
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作者：Luo, Wei
作者单位：Zhejiang University
摘要：Efficient dimension reduction regarding the interaction between two response variables, which facilitates statistical analysis in multiple important application scenarios, was initially discussed by Luo (J. R. Stat. Soc. Ser. B. spaces were introduced, and, under mild conditions on the predictor, they were equated with the family of dual inverse regression subspaces. Besides the general framework, however, limited theory has been proposed to uncover the mystery of these spaces. In this paper, ...
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作者：Bellec, Pierre c.
作者单位：State University System of Florida; Florida State University
摘要：We consider observations (X, y) from single index models with unknown link function, Gaussian covariates and a regularized M-estimator beta constructed from convex loss function and regularizer. In the regime where sample size n and dimension p are both increasing such that p/n has a finite limit, the behavior of the empirical distribution of beta and the predicted values X beta has been previously characterized in a number of models: The empirical distributions are known to converge to proxim...
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作者：Jiang, Kuanhao; Mukherjee, Rajarshi; Sen, Subhabrata; Sur, Pragya
作者单位：Harvard University; Harvard University; Harvard T.H. Chan School of Public Health
摘要：Estimation of the average treatment effect (ATE) is a central problem in causal inference. In recent times, inference for the ATE in the presence of high-dimensional covariates has been extensively studied. Among diverse approaches that have been proposed, augmented inverse propensity weighting (AIPW) with cross-fitting has emerged a popular choice in practice. In this work, we study this cross-fit AIPW estimator under well-specified outcome regression and propensity score models in a high-dim...
