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作者：Giordano, Matteo; Wang, Sven
作者单位：University of Turin; Humboldt University of Berlin
摘要：We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of the likelihood and its gradient, and computational methods have thus far largely resorted to expensive simulation-based techniques. In this article, we propose a new computational approach which is motivated by PDE theory and is built around the characterisat...
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作者：Kotekal, Subhodh; Gao, Chao
作者单位：University of Chicago
摘要：We study estimation of an s-sparse signal in the p-dimensional Gaussian sequence model with equicorrelated observations and derive the minimax rate. A new phenomenon emerges from correlation, namely, the rate scales with respect to p-2s and exhibits a phase transition at p-2s asymptotic to root root p root p. Correlation is shown to be a blessing, provided it is sufficiently strong and the critical correlation level exhibits a delicate dependence on the sparsity level. Due to correlation, the ...
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作者：Cattaneo, Matias D.; Yu, Ruiqi Rae
作者单位：Princeton University
摘要：This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on d-variate random vectors (d >= 1). First, a uniform Gaussian strong approximation is established for general empirical processes indexed by possibly Lipschitz functions, improving on previous results in the literature. In the setting considered by Rio (Probab. Theory Related Fields 98 (1994) 21-45), and if the function class is Lipschitzian, our result improves the ap...
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作者：Morikawa, Kosuke; Terada, Yoshikazu; Kim, Jae Kwang
作者单位：University of Osaka; RIKEN; Iowa State University
摘要：In probability sampling, sampling weights are often used to remove selection bias in the sample. The Horvitz-Thompson estimator is well known to be consistent and asymptotically normally distributed; however, it is not necessarily efficient. This study derives the semiparametric efficiency bound for various target parameters by considering the survey weights as random variables and consequently proposes two semiparametric estimators with working models on the survey weights. One estimator assu...
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作者：Brown, Benjamin; Zhang, Kai; Meng, Xiao-Li
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; Harvard University
摘要：Two linearly uncorrelated binary variables must be also independent because nonlinear dependence cannot manifest with only two possible states. This inherent linearity is the atom of dependency constituting any complex form of relationship. Inspired by this observation, we develop a framework called binary expansion linear effect (BELIEF) for understanding arbitrary relationships with a binary outcome. Models from the BELIEF framework are easily interpretable because they describe the associat...
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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：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：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...
