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作者：Chan, Hock Peng
作者单位：National University of Singapore
摘要：Lai and Robbins (Adv. in Appl. Math. 6 (1985) 4-22) and Lai (Ann. Statist. 15 (1987) 1091-1114) provided efficient parametric solutions to the multi-armed bandit problem, showing that arm allocation via upper confidence bounds (UCB) achieves minimum regret. These bounds are constructed from the Kullback-Leibler information of the reward distributions, estimated from specified parametric families. In recent years, there has been renewed interest in the multi-armed bandit problem due to new appl...
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作者：Lee, Stephen M. S.; Yang, Puyudi
作者单位：University of Hong Kong; University of California System; University of California Davis
摘要：Suppose that a confidence region is desired for a subvector theta of a multidimensional parameter xi = (theta, psi), based on an M-estimator (xi) over cap (n) = ((theta) over cap (n )= (psi) over cap (n)) calculated from a random sample of size n. Under nonstandard conditions (xi) over cap (n) often converges at a nonregular rate (xi) over cap (n), in which case consistent estimation of the distribution of r(n) ((theta) over cap (n) - theta), a pivot commonly chosen for confidence region const...
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作者：Zou, Changliang; Wang, Guanghui; Li, Runze
作者单位：Nankai University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and the optimal penalizat...
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作者：Guntuboyina, Adityanand; Lieu, Donovan; Chatterjee, Sabyasachi; Sen, Bodhisattva
作者单位：University of California System; University of California Berkeley; University of Illinois System; University of Illinois Urbana-Champaign; Columbia University
摘要：We study trend filtering, a relatively recent method for univariate nonparametric regression. For a given integer r >= 1, the rth order trend filtering estimator is defined as the minimizer of the sum of squared errors when we constrain (or penalize) the sum of the absolute rth order discrete derivatives of the fitted function at the design points. For r = 1, the estimator reduces to total variation regularization which has received much attention in the statistics and image processing literat...
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作者：Kolaczyk, Eric D.; Lin, Lizhen; Rosenberg, Steven; Walters, Jackson; Xu, Jie
作者单位：Boston University; University of Notre Dame
摘要：It is becoming increasingly common to see large collections of network data objects, that is, data sets in which a network is viewed as a fundamental unit of observation. As a result, there is a pressing need to develop network-based analogues of even many of the most basic tools already standard for scalar and vector data. In this paper, our focus is on averages of unlabeled, undirected networks with edge weights. Specifically, we (i) characterize a certain notion of the space of all such net...
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作者：Koltchinskii, Vladimir; Loffler, Matthias; Nickl, Richard
作者单位：University System of Georgia; Georgia Institute of Technology; University of Cambridge
摘要：We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations X-1, ..., X-n in a separable Hilbert space H with unknown covariance operator Sigma. The complexity of the problem is characterized by its effective rank r(Sigma) := tr(Sigma)/parallel to Sigma parallel to where tr(Sigma) denotes the trace of Sigma and parallel to Sigma parallel to denotes its operator norm. We develop a method of bias reduction in the problem of estimation of linear functionals of eigenvect...
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作者：Tan, Kai; Shi, Lei; Yu, Zhou
作者单位：East China Normal University; Fudan University
摘要：Sliced inverse regression (SIR) is an innovative and effective method for sufficient dimension reduction and data visualization. Recently, an impressive range of penalized SIR methods has been proposed to estimate the central subspace in a sparse fashion. Nonetheless, few of them considered the sparse sufficient dimension reduction from a decision-theoretic point of view. To address this issue, we in this paper establish the minimax rates of convergence for estimating the sparse SIR directions...
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作者：Wang, Xiaoqin; Yin, Li
作者单位：University of Gavle; Karolinska Institutet
摘要：In sequential causal inference, two types of causal effects are of practical interest, namely, the causal effect of the treatment regime (called the sequential causal effect) and the blip effect of treatment on the potential outcome after the last treatment. The well-known G-formula expresses these causal effects in terms of the standard parameters. In this article, we obtain a new G-formula that expresses these causal effects in terms of the point observable effects of treatments similar to t...
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作者：Schweinberger, Michael; Stewart, Jonathan
作者单位：Rice University
摘要：Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple example of a random graph with additional structure is a random graph with neighborhoods and local dependence within neighborhoods. We develop the first concentration and consistency results for maximum likelihood and M-estimators of a wide range of canonical and ...
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作者：Koskela, Jere; Jenkins, Paul A.; Johansen, Adam M.; Spano, Dario
作者单位：University of Warwick; University of Warwick
摘要：We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied statistics and cognate disciplines. We consider the genealogical tree embedded into such particle systems, and identify conditions, as well as an appropriate time-scaling, under which they converge to the Kingman n-coalescent in the infinite system size limit i...
