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作者：Nickl, Richard; Pavliotis, Grigorios A.; Ray, Kolyan
作者单位：University of Cambridge; Imperial College London
摘要：We consider nonparametric statistical inference on a periodic interaction potential W from noisy discrete space-time measurements of solutions rho = rho W of the nonlinear McKean-Vlasov equation, describing the probability density of the mean field limit of an interacting particle system. We show how Gaussian process priors assigned to W give rise to posterior mean estimators that exhibit fast convergence rates for the implied estimated densities rho towards rho W . We further show that if the...
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作者：Luo, Lan; Shi, Chengchun; Wang, Jitao; Wi, Zhenke; Li, Lexin
作者单位：Rutgers University System; Rutgers University New Brunswick; University of London; London School Economics & Political Science; University of Michigan System; University of Michigan; University of California System; University of California Berkeley
摘要：Mediation analysis is an important analytic tool commonly used in a broad range of scientific applications. In this article, we study the problem of mediation analysis when there are multivariate and conditionally dependent mediators, and when the variables are observed over multiple time points. The problem is challenging, because the effect of a mediator involves not only the path from the treatment to this mediator itself at the current time point, but also all possible paths pointed to thi...
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作者：Legramanti, Sirio; Durante, Daniele; Alquier, Pierre
作者单位：University of Bergamo; Bocconi University; Bocconi University; ESSEC Business School
摘要：There has been an increasing interest on summary-free solutions for approximate Bayesian computation (ABC) that replace distances among summaries with discrepancies between the empirical distributions of the observed data and the synthetic samples generated under the proposed parameter values. The success of these strategies has motivated theoretical studies on the limiting properties of the induced posteriors. However, there is still the lack of a theoretical framework for summary-free ABC th...
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作者：Bhattacharjee, Satarupa; Li, Bing; Xue, Lingzhou
作者单位：State University System of Florida; University of Florida; Florida State University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：Random objects are complex non-Euclidean data taking values in general metric spaces, possibly devoid of any underlying vector space structure. Such data are becoming increasingly abundant with the rapid advancement in technology. Examples include probability distributions, positive semidefinite matrices and data on Riemannian manifolds. However, except for regression for object-valued response with Euclidean predictors and distributionon-distribution regression, there has been limited develop...
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作者：Kotekal, Subhodh; Kundu, Soumyabrata
作者单位：University of Chicago
摘要：Heteroskedasticity testing in nonparametric regression is a classic statistical problem with important practical applications, yet fundamental limits are unknown. Adopting a minimax perspective, this article considers the testing problem in the context of an alpha-H & ouml;lder mean and a beta-H & ouml;lder variance function. For alpha > 0 and beta is an element of (0, 1/2), the sharp minimax separation rate n(-4 alpha) + n(-4 beta /(4 beta+1)) + n(-2 beta )is established. To achieve the minim...
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作者：Ignatiadis, Nikolaos; Sen, Bodhisattva
作者单位：University of Chicago; University of Chicago; Columbia University
摘要：A common task in high-throughput biology is to screen for associations across thousands of units of interest, for example, genes or proteins. Often, the data for each unit are modeled as Gaussian measurements with unknown mean and variance and are summarized as per-unit sample averages and sample variances. The downstream goal is multiple testing for the means. In this domain, it is routine to moderate (i.e., to shrink) the sample variances through parametric empirical Bayes methods before com...
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作者：Chong, Carsten H.; Delerue, Thomas; Mies, Fabian
作者单位：Hong Kong University of Science & Technology; Delft University of Technology
摘要：Consider the sum Y = B + B(H) of a Brownian motion B and an independent fractional Brownian motion B(H) with Hurst parameter H is an element of (0, 1). Even though B(H) is not a semimartingale, it was shown by Cheridito (Bernoulli 7 (2001) 913-934) that Y is a semimartingale if H > 3/4. Moreover, Y is locally equivalent to B in this case, so H cannot be consistently estimated from local observations of Y. This paper pivots on another unexpected feature in this model: if B and B(H) become corre...
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作者：Shen, Yinan; Li, Jingyang; Cai, Jian-feng; Xia, Dong
作者单位：Hong Kong University of Science & Technology
摘要：High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since the robust loss functions are usually nonsmooth. More recently, computationally fast nonconvex approaches via subgradient descent are proposed, which, unfortunately, fail to deliver a statistically consistent estimator even under sub-Gaussian n...
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作者：Li, Xiang; Ruan, Feng; Wang, Huiyuan; Long, Qi; Su, Weijie J.
作者单位：University of Pennsylvania; Northwestern University
摘要：Since ChatGPT was introduced in November 2022, embedding (nearly) unnoticeable statistical signals into text generated by large language models (LLMs), also known as watermarking, has been used as a principled approach to provable detection of LLM-generated text from its human-written counterpart. In this paper, we introduce a general and flexible framework for reasoning about the statistical efficiency of watermarks and designing powerful detection rules. Inspired by the hypothesis testing fo...
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作者：Barigozzi, Matteo; LA Vecchia, Davide; Liu, Hang
作者单位：Institut Polytechnique de Paris; ENSAE Paris; University of Geneva; Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：Motivated by the need for analysing large spatio-temporal panel data, we introduce a novel nonparametric methodology for n-dimensional random fields observed across S spatial locations and T time periods. We call it general spatio-temporal factor model (GSTFM). First, we provide the probabilistic and mathematical underpinning needed for the representation of a random field as the sum of two components: the common component (driven by a small number q of latent factors) and the idiosyncratic co...
