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作者：Lee, Eun Ryung; Park, Seyoung; Mammen, Enno; Park, Byeong U.
作者单位：Sungkyunkwan University (SKKU); Yonsei University; Ruprecht Karls University Heidelberg; Seoul National University (SNU)
摘要：Smooth backfitting has been proposed and proved as a powerful nonparametric estimation technique for additive regression models in various settings. Existing studies are restricted to cases with a moderate number of covariates and are not directly applicable to high dimensional settings. In this paper, we develop new kernel estimators based on the idea of smooth backfitting for high dimensional additive models. We introduce a novel penalization scheme, combining the idea of functional Lasso wi...
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作者：Luedtke, Alex; Chung, Incheoul
作者单位：University of Washington; University of Washington Seattle
摘要：We present estimators for smooth Hilbert-valued parameters, where smoothness is characterized by a pathwise differentiability condition. When the parameter space is a reproducing kernel Hilbert space, we provide a means to obtain efficient, root-n n rate estimators and corresponding confidence sets. These estimators correspond to generalizations of cross-fitted one-step estimators based on Hilbert-valued efficient influence functions. We give theoretical guarantees even when arbitrary estimato...
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作者：Qiu, Hongxiang; Tchetgen, Eric Tchetgen; Dobriban, Edgar
作者单位：Michigan State University; University of Pennsylvania
摘要：Statistical machine learning methods often face the challenge of limited data available from the population of interest. One remedy is to leverage data from auxiliary source populations, which share some conditional distributions or are linked in other ways with the target domain. Techniques leveraging such dataset shift conditions are known as domain adaptation or transfer learning. . Despite extensive literature on dataset shift, limited works address how to efficiently use the auxiliary pop...
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作者：Cattaneo, Matias D.; Jansson, Michael; Nagasawa, Kenichi
作者单位：Princeton University; University of California System; University of California Berkeley; University of Warwick
摘要：Westling and Carone ( Ann. Statist. 48 (2020) 1001-1024) proposed a framework for studying the large sample distributional properties of generalized Grenander-type estimators, a versatile class of nonparametric estimators of monotone functions. The limiting distribution of those estimators is representable as the left derivative of the greatest convex minorant of a Gaussian process whose monomial mean can be of unknown order (when the degree of flatness of the function of interest is unknown)....
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作者：Li, Degui; Li, Runze; Shang, Han Lin
作者单位：University of Macau; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Macquarie University
摘要：We consider detecting and estimating breaks in heterogenous mean functions of high-dimensional functional time series which are allowed to be cross-sectionally correlated. A new test statistic combining the functional CUSUM statistic and power enhancement component is proposed with asymptotic null distribution comparable to the conventional CUSUM theory derived for a single functional time series. In particular, the extra power enhancement component enlarges the region where the proposed test ...
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作者：Rousseau, Judith; Scricciolo, Catia
作者单位：University of Oxford; University of Verona
摘要：We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors with independent coordinates having ordinary smooth densities, we derive an inversion inequality relating the L-1-Wasserstein distance between two distributions of the signal to the L-1-distance between the corresponding mixture densities of the observations. ...
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作者：Nickl, Richard; Titi, Edriss s.
作者单位：University of Cambridge; University of Cambridge
摘要：We consider a nonlinear Bayesian data assimilation model for the periodic two-dimensional Navier-Stokes equations with initial condition modelled by a Gaussian process prior. We show that if the system is updated with sufficiently many discrete noisy measurements of the velocity field, then the posterior distribution eventually concentrates near the ground truth solution of the time evolution equation, and in particular that the initial condition is recovered consistently by the posterior mean...
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作者：Zhang, Zhengxin; Goldfeld, Ziv; Mroueh, Youssef; Sriperumbudur, Bharath K.
作者单位：Cornell University; Cornell University; International Business Machines (IBM); IBM USA; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：The Gromov-Wasserstein (GW) distance, rooted in optimal transport (OT) theory, quantifies dissimilarity between metric measure spaces and provides a framework for aligning heterogeneous datasets. While computational aspects of the GW problem have been widely studied, a duality theory and fundamental statistical questions concerning empirical convergence rates remained obscure. This work closes these gaps for the quadratic GW distance over Euclidean spaces of different dimensions dx x and d y ....
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作者：Altmeyer, Randolf; Tiepner, Anton; Wahl, Martin
作者单位：University of Cambridge; Aarhus University; University of Bielefeld
摘要：The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of measurements is nondecreasing, the rate of convergence for each coefficient depends on its differential order and is faster for higher order coefficients. Based on an explicit analysis of the reproducing kernel Hilbert space of a general stochastic evolution equation...
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作者：Doss, Charles R.; Weng, Guangwei; Wang, Lan; Moscovice, Ira; Chantarat, Tongtan
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Miami; University of Minnesota System; University of Minnesota Twin Cities
摘要：The vast majority of literature on evaluating the significance of a treatment effect based on observational data has been confined to discrete treatments. These methods are not applicable to drawing inference for a continuous treatment, which arises in many important applications. To adjust for confounders when evaluating a continuous treatment, existing inference methods often rely on discretizing the treatment or using (possibly misspecified) parametric models for the effect curve. Recently,...
