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作者：He, Hera Y.; Basu, Kinjal; Zhao, Qingyuan; Owen, Art B.
作者单位：Stanford University; University of Pennsylvania
摘要：It is common for genomic data analysis to use p-values from a large number of permutation tests. The multiplicity of tests may require very tiny p-values in order to reject any null hypotheses and the common practice of using randomly sampled permutations then becomes very expensive. We propose an inexpensive approximation to p-values for two sample linear test statistics, derived from Stolarsky's invariance principle. The method creates a geometrically derived reference set of approximate p-v...
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作者：Ramdas, Aaditya K.; Barber, Rina F.; Wainwright, Martin J.; Jordan, Michael, I
作者单位：Carnegie Mellon University; University of Chicago; University of California System; University of California Berkeley
摘要：There is a significant literature on methods for incorporating knowledge into multiple testing procedures so as to improve their power and precision. Some common forms of prior knowledge include (a) beliefs about which hypotheses are null, modeled by nonuniform prior weights; (b) differing importances of hypotheses, modeled by differing penalties for false discoveries; (c) multiple arbitrary partitions of the hypotheses into (possibly overlapping) groups and (d) knowledge of independence, posi...
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作者：Bobkov, Sergey G.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; HSE University (National Research University Higher School of Economics)
摘要：Let F-n denote the distribution function of the normalized sum of n i.i.d. random variables. In this paper, polynomial rates of approximation of F n by the corrected normal laws are considered in the model where the underlying distribution has a convolution structure. As a basic tool, the convergence part of Khinchine's theorem in metric theory of Diophantine approximations is extended to the class of product characteristic functions.
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作者：Lin, Yi; Martin, Ryan; Yang, Min
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; North Carolina State University
摘要：Classically, Fisher information is the relevant object in defining optimal experimental designs. However, for models that lack certain regularity, the Fisher information does not exist, and hence, there is no notion of design optimality available in the literature. This article seeks to fill the gap by proposing a so-called Hellinger information, which generalizes Fisher information in the sense that the two measures agree in regular problems, but the former also exists for certain types of no...
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作者：Zhu, Ke
作者单位：University of Hong Kong
摘要：This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute deviations estimator (LADE) for the model. Second, we develop the random weighting (RW) method to estimate its asymptotic covariance matrix, leading to the implementation of the Wald test. Third, we construct a portmanteau test for model checking, and use the RW me...
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作者：Chen, Ningyuan; Lee, Donald K. K.; Negahban, Sahand N.
作者单位：Hong Kong University of Science & Technology; Hong Kong University of Science & Technology; Yale University; Yale University; Yale University
摘要：Exploiting the fact that most arrival processes exhibit cyclic behaviour, we propose a simple procedure for estimating the intensity of a nonhomogeneous Poisson process. The estimator is the super-resolution analogue to Shao (2010) and Shao and Lii [J. R. Stat. Soc. Ser. B. Stat. Methodol. 73 (2011) 99-122], which is a sum of p sinusoids where p and the amplitude and phase of each wave are not known and need to be estimated. This results in an interpretable yet flexible specification that is s...
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作者：Athey, Susan; Tibshirani, Julie; Wager, Stefan
作者单位：Stanford University
摘要：We propose generalized random forests, a method for nonparametric statistical estimation based on random forests (Breiman [Mach. Learn. 45 (2001) 5-32]) that can be used to fit any quantity of interest identified as the solution to a set of local moment equations. Following the literature on local maximum likelihood estimation, our method considers a weighted set of nearby training examples; however, instead of using classical kernel weighting functions that are prone to a strong curse of dime...
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作者：Cape, Joshua; Minh Tang; Priebe, Carey E.
作者单位：Johns Hopkins University
摘要：The singular value matrix decomposition plays a ubiquitous role throughout statistics and related fields. Myriad applications including clustering, classification, and dimensionality reduction involve studying and exploiting the geometric structure of singular values and singular vectors. This paper provides a novel collection of technical and theoretical tools for studying the geometry of singular subspaces using the two-to-infinity norm. Motivated by preliminary deterministic Procrustes anal...
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作者：Tan, Zhiqiang; Zhang, Cun-Hui
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive regression where functional semi-norms are used to induce smoothness of component functions and the empirical L-2 norm is used to induce sparsity. The functional semi-norms can be of Sobolev or bounded variation types and are allowed to be different amongst i...
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作者：Berrett, Thomas B.; Samworth, Richard J.; Yuan, Ming
作者单位：University of Cambridge; University of Wisconsin System; University of Wisconsin Madison
摘要：Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seek entropy estimators that are efficient and achieve the local asymptotic minimax lower bound with respect to squared error loss. To this end, we study weighted averages of the estimators originally proposed by Kozachenko and Leonenko [Probl. Inform. Transm. 23 (1987), 95-101], based on the k-nearest...
