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作者：Dicker, Lee H.; Erdogdu, Murat A.
作者单位：Rutgers University System; Rutgers University New Brunswick; Stanford University
摘要：We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models. Random-effects models and variance components estimation are classical topics in statistics, with a corresponding well-established asymptotic theory. However, our finite sample results for quadratic forms provide additional flexibility for easily analyzing rand...
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作者：Kong, Weihao; Valiant, Gregory
作者单位：Stanford University
摘要：We consider the problem of approximating the set of eigenvalues of the covariance matrix of a multivariate distribution (equivalently, the problem of approximating the population spectrum), given access to samples drawn from the distribution. We consider this recovery problem in the regime where the sample size is comparable to, or even sublinear in the dimensionality of the distribution. First, we propose a theoretically optimal and computationally efficient algorithm for recovering the momen...
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作者：Han, Dong; Tsung, Fugee; Xian, Jinguo
作者单位：Shanghai Jiao Tong University; Hong Kong University of Science & Technology
摘要：By introducing suitable loss random variables of detection, we obtain optimal tests in terms of the stopping time or alarm time for Bayesian changepoint detection not only for a general prior distribution of change-points but also for observations being a Markov process. Moreover, the optimal (minimal) average detection delay is proved to be equal to 1 for any (possibly large) average run length to false alarm if the number of possible change-points is finite.
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作者：Kong, Yinfei; Li, Daoji; Fan, Yingying; Lv, Jinchi
作者单位：California State University System; California State University Fullerton; State University System of Florida; University of Central Florida; University of Southern California
摘要：Feature interactions can contribute to a large proportion of variation in many prediction models. In the era of big data, the coexistence of high dimensionality in both responses and covariates poses unprecedented challenges in identifying important interactions. In this paper, we suggest a two-stage interaction identification method, called the interaction pursuit via distance correlation (IPDC), in the setting of high-dimensional multi-response interaction models that exploits feature screen...
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作者：Chernozhukov, Victor; Galichon, Alfred; Hallin, Marc; Henry, Marc
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); New York University; New York University; Institut d'Etudes Politiques Paris (Sciences Po); Universite Libre de Bruxelles; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We propose new concepts of statistical depth, multivariate quantiles, vector quantiles and ranks, ranks and signs, based on canonical transportation maps between a distribution of interest on R-d and a reference distribution on the d-dimensional unit ball. The new depth concept, called Monge Kantorovich depth, specializes to halfspace depth for d = 1 and in the case of spherical distributions, but for more general distributions, differs from the latter in the ability for its contours to accoun...
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作者：Li, Zeng; Wang, Qinwen; Yao, Jianfeng
作者单位：University of Hong Kong
摘要：Identifying the number of factors in a high-dimensional factor model has attracted much attention in recent years and a general solution to the problem is still lacking. A promising ratio estimator based on singular values of lagged sample auto-covariance matrices has been recently proposed in the literature with a reasonably good performance under some specific assumption on the strength of the factors. Inspired by this ratio estimator and as a first main contribution, this paper proposes a c...
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作者：Chambaz, Antoine; Zheng, Wenjing; van der Laan, Mark J.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：This article studies the targeted sequential inference of an optimal treatment rule (TR) and its mean reward in the nonexceptional case, that is, assuming that there is no stratum of the baseline covariates where treatment is neither beneficial nor harmful, and under a companion margin assumption. Our pivotal estimator, whose definition hinges on the targeted minimum loss estimation (TMLE) principle, actually infers the mean reward under the current estimate of the optimal TR. This data-adapti...
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作者：Metelkina, Asya; Pronzato, Luc
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：Covariate-adaptive treatment allocation is considered in the situation when a compromise must be made between information (about the dependency of the probability of success of each treatment upon influential covariates) and cost (in terms of number of subjects receiving the poorest treatment). Information is measured through a design criterion for parameter estimation, the cost is additive and is related to the success probabilities. Within the framework of approximate design theory, the dete...
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作者：Su, Weijie; Bogdan, Malgorzata; Candes, Emmanuel
作者单位：University of Pennsylvania; University of Wroclaw; Stanford University; Stanford University
摘要：In regression settings where explanatory variables have very low correlations and there are relatively few effects, each of large magnitude, we expect the Lasso to find the important variables with few errors, if any. This paper shows that in a regime of linear sparsity-meaning that the fraction of variables with a nonvanishing effect tends to a constant, however small-this cannot really be the case, even when the design variables are stochastically independent. We demonstrate that true featur...
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作者：Todorov, Viktor
作者单位：Northwestern University
摘要：In this paper, we propose a test for deciding whether the jump activity index of a discretely observed It semimartingale of pure-jump type (i.e., one without a diffusion) varies over a fixed interval of time. The asymptotic setting is based on observations within a fixed time interval with mesh of the observation grid shrinking to zero. The test is derived for semimartingales whose spot jump compensator around zero is like that of a stable process, but importantly the stability index can vary...
