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作者：Chong, Carsten
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at high temporal frequency, we use limit theorems for multipower variations and related functionals to construct consistent nonparametric estimators and asymptotic confidence bounds for the integrated volatility process. As a byproduct of our analysis, we also obtain feasible estimators for the regularity of the spatial covariance function of...
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作者：Hopkins, Samuel B.
作者单位：University of California System; University of California Berkeley
摘要：We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector X has finite mean and covariance. In this setting, the radius of confidence intervals achieved by the empirical mean are large compared to the case that X is Gaussian or sub-Gaussian. We offer the first polynomial time algorithm to estimate the mean with sub-Gaussian-size confidence intervals under such mild assumptions. Our algorithm is based on a new...
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作者：Lecue, Guillaume; Lerasle, Matthieu
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Ecole Polytechnique; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：Median-of-means (MOM) based procedures have been recently introduced in learning theory (Lugosi and Mendelson (2019); Lecue and Lerasle (2017)). These estimators outperform classical least-squares estimators when data are heavy-tailed and/or are corrupted. None of these procedures can be implemented, which is the major issue of current MOM procedures (Ann. Statist. 47 (2019) 783-794). In this paper, we introduce minmax MOM estimators and show that they achieve the same sub-Gaussian deviation b...
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作者：Dette, Holger; Kokot, Kevin; Aue, Alexander
作者单位：Ruhr University Bochum; University of California System; University of California Davis
摘要：Functional data analysis is typically conducted within the L-2-Hilbert space framework. There is by now a fully developed statistical toolbox allowing for the principled application of the functional data machinery to real-world problems, often based on dimension reduction techniques such as functional principal component analysis. At the same time, there have recently been a number of publications that sidestep dimension reduction steps and focus on a fully functional L-2-methodology. This pa...
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作者：Jagadeesan, Ravi; Pillai, Natesh S.; Volfovsky, Alexander
作者单位：Harvard University; Harvard University; Duke University
摘要：In this paper, we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide ran...
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作者：Saha, Sujayam; Guntuboyina, Adityanand
作者单位：University of California System; University of California Berkeley
摘要：We study the nonparametric maximum likelihood estimator (NPMLE) for estimating Gaussian location mixture densities in d-dimensions from independent observations. Unlike usual likelihood-based methods for fitting mixtures, NPMLEs are based on convex optimization. We prove finite sample results on the Hellinger accuracy of every NPMLE. Our results imply, in particular, that every NPMLE achieves near parametric risk (up to logarithmic multiplicative factors) when the true density is a discrete Ga...
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作者：Xi, Haokai; Yang, Fan; Yin, Jun
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Los Angeles
摘要：The eigenvector empirical spectral distribution (VESD) is a useful tool in studying the limiting behavior of eigenvalues and eigenvectors of covariance matrices. In this paper, we study the convergence rate of the VESD of sample covariance matrices to the deformed Marcenko-Pastur (MP) distribution. Consider sample covariance matrices of the form Sigma(XX)-X-1/2* Sigma(1/2), where X = (x(ij)) is an M x N random matrix whose entries are independent random variables with mean zero and variance N-...
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作者：Westling, Ted; Carone, Marco
作者单位：University of Pennsylvania; University of Washington; University of Washington Seattle
摘要：The problem of nonparametric inference on a monotone function has been extensively studied in many particular cases. Estimators considered have often been of so-called Grenander type, being representable as the left derivative of the greatest convex minorant or least concave majorant of an estimator of a primitive function. In this paper, we provide general conditions for consistency and pointwise convergence in distribution of a class of generalized Grenander-type estimators of a monotone fun...
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作者：Lopes, Miles E.; Lin, Zhenhua; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：In recent years, bootstrap methods have drawn attention for their ability to approximate the laws of max statistics in high-dimensional problems. A leading example of such a statistic is the coordinatewise maximum of a sample average of n random vectors in R-p. Existing results for this statistic show that the bootstrap can work when n << p, and rates of approximation (in Kolmogorov distance) have been obtained with only logarithmic dependence in p. Nevertheless, one of the challenging aspects...
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作者：Maruyama, Yuzo; Strawderman, William E.
作者单位：University of Tokyo; Rutgers University System; Rutgers University New Brunswick
摘要：This paper investigates estimation of the mean vector under invariant quadratic loss for a spherically symmetric location family with a residual vector with density of the form f (x, u) = eta((p+ n)/2) f (eta{parallel to x - theta parallel to(2) + parallel to u parallel to(2)}), where. is unknown. We show that the natural estimator x is admissible for p = 1, 2. Also, for p >= 3, we find classes of generalized Bayes estimators that are admissible within the class of equivariant estimators of th...
