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作者：Lahiry, Samriddha; Nussbaum, Michael
作者单位：Cornell University; Cornell University
摘要：In classical statistics, Pinsker's theorem provides an exact asymptotic minimax bound in nonparametric estimation, improving upon optimal rates of convergence results. We obtain a quantum version of the theorem by establishing asymptotic minimax results for estimation of the displacement vector in a quantum Gaussian white noise model, given by a sequence of shifted vacuum states. Analogous results are then obtained for estimation of a general pure state from an ensemble of identically prepared...
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作者：Zhao, Anqi; Ding, Peng
作者单位：National University of Singapore; University of California System; University of California Berkeley
摘要：The split-plot design arose from agricultural science with experimental units, also known as the subplots, nested within groups known as the whole plots. It assigns different interventions at the whole-plot and subplot levels, respectively, providing a convenient way to accommodate hard-to-change factors. By design, subplots within the same whole plot receive the same level of the whole-plot intervention, and thereby induce a group structure on the final treatment assignments. A common strateg...
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作者：Chi, Chien-Ming; Vossler, Patrick; Fan, Yingying; Lv, Jinchi
作者单位：Academia Sinica - Taiwan; University of Southern California
摘要：As a flexible nonparametric learning tool, the random forests algorithm has been widely applied to various real applications with appealing empirical performance, even in the presence of high-dimensional feature space. Unveil-ing the underlying mechanisms has led to some important recent theoretical results on the consistency of the random forests algorithm and its variants. However, to our knowledge, almost all existing works concerning random forests consistency in a high-dimensional setting...
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作者：Chronopoulos, Ilias; Giraitis, Liudas; Kapetanios, George
作者单位：University of Essex; University of London; Queen Mary University London; University of London; King's College London
摘要：This paper suggests a multiplicative volatility model where volatility is decomposed into a stationary and a nonstationary persistent part. We pro -vide a testing procedure to determine which type of volatility is prevalent in the data. The persistent part of volatility is associated with a nonstation-ary persistent process satisfying some smoothness and moment conditions. The stationary part is related to stationary conditional heteroskedasticity. We outline theory and conditions that allow t...
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作者：Oh, Eun Jeong; Qian, Min; Cheung, Ying Kuen
作者单位：Columbia University
摘要：A dynamic treatment regime (DTR) is a sequence of decision rules, one per stage of intervention, that maps up-to-date patient information to a recommended treatment. Discovering an appropriate DTR for a given disease is a challenging issue especially when a large set of prognostic variables are observed. To address this problem, we propose penalized regression-based learning methods with l(1) penalty to estimate the optimal DTR that would maximize the expected outcome if implemented. We also p...
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作者：Cheysson, Felix; Lang, Gabriel
作者单位：INRAE; Universite Paris Saclay; AgroParisTech
摘要：This paper presents a parametric estimation method for ill-observed linear stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, methods based on the likelihood are not feasible. We show that spectral estimation based on Whittle's method is adapted to this case and provides consistent and asymptotically normal estimators, provided a mild moment condition on the reproduction function. Simulated data sets and a case-s...
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作者：Gao, Lan; Shao, Qi-Man; Shi, Jiasheng
作者单位：Chinese University of Hong Kong; Southern University of Science & Technology; University of Southern California; University of Pennsylvania
摘要：Let {(Xi, Yi)}(i=1)(n) be a sequence of independent bivariate random vec- tors. In this paper, we establish a refined Cramer-type moderate deviation theorem for the general self-normalized sum Sigma(n)(i=1) X-i/(Sigma(n)(i=1) Y-i(2))(1/2), which unifies and extends the classical Cramer (Actual. Sci. Ind. 736 (1938) 5-23) theorem and the self-normalized Cramer-type moderate deviation theorems by Jing, Shao and Wang (Ann. Probab. 31 (2003) 2167-2215) as well as the further refined version by Wan...
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作者：Hastie, Trevor; Montanari, Andrea; Rosset, Saharon; Tibshirani, Ryan J.
作者单位：Stanford University; Stanford University; Stanford University; Tel Aviv University; Carnegie Mellon University; Carnegie Mellon University
摘要：Interpolators-estimators that achieve zero training error-have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum l(2) norm (ridgeless) interpolation least squares regression, focusing on the high-dimensional regime in which the number of unknown parameters p is of the same order as the number of samples n. We consider two different models for the feature distribution: a linear model...
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作者：Chen, Yen-Chi
作者单位：University of Washington; University of Washington Seattle
摘要：We introduce the concept of pattern graphs-directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a missing not at random restriction. We introduce a selection model and a pattern mixture model formulations using the pattern graphs and show that they are equivalent. A pattern graph leads to an inverse probability weighting estimator as well as an imputation-base...
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作者：Argiento, Raffaele; De Iorio, Maria
作者单位：University of Bergamo; National University of Singapore
摘要：Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. Following a Bayesian nonparametric perspective, we introduce a new class of priors: the Normalized Independent Point Process. We investigate the probabilistic properties of this new class and present many special cases. In particular, we provide an explicit formula for the distribution of the implied partition, as well as the posterior characterization of the new process in t...
