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作者：Chen, Xiaohong; Hong, Han; Tarozzi, Alessandro
作者单位：Yale University; Stanford University; Duke University
摘要：We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database, when such distribution is common to the two data sets. The auxiliary sample can be independent of the primary sample, or can be a subset of it. Fo...
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作者：Barron, Andrew R.; Cohen, Albert; Dahmen, Wolfgang; DeVore, Ronald A.
作者单位：Yale University; Sorbonne Universite; Universite Paris Cite; RWTH Aachen University; University of South Carolina System; University of South Carolina Columbia
摘要：We consider the problem of approximating a given element f from a Hilbert space H by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the existing theory of convergence rates for both the orthogonal greedy algorithm and the relaxed greedy algorithm, as well as for the forward stepwise projection algorithm. For all these algorithms, we prove convergence results for a variety of function classes and not simp...
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作者：Guo, Hongwen; Koul, Hira L.
作者单位：Michigan State University
摘要：This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple linear regression model, the first-order asymptotic distribution of the least square estimator of the slope parameter is observed to be degenerate. However, in the second order, this estimator is n(1/2)-consistent and asymptotically normal for h + H < 3/2; nonnor...
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作者：Hall, Peter; Jin, Jiashun
作者单位：University of Melbourne; University of California System; University of California Davis; Purdue University System; Purdue University
摘要：The problem of signal detection using sparse, faint information is closely related to a variety of contemporary statistical problems, including the control of false-discovery rate, and classification using very high-dimensional data. Each problem can be solved by conducting a large number of simultaneous hypothesis tests, the properties of which are readily accessed under the assumption of independence. In this paper we address the case of dependent data, in the context of higher criticism met...
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作者：Papaspiliopoulos, Omiros; Roberts, Gareth
作者单位：University of Warwick
摘要：We characterize the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence can be uniform, geometric or subgeometric depending on the relative tail behavior of the error distributions, and on the parametrization chosen. Our theory is applied to characterize the convergence of the Gibbs sampler on latent Gaussian process models. We...
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作者：Fan, Jianqing; Fan, Yingying
作者单位：Princeton University; University of Southern California; Harvard University
摘要：Classification using high-dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high-throughput data. The impact of dimensionality on classifications is poorly understood. In a seminal paper, Bickel and Levina [Bernoulli 10 (2004) 989-1010] show that the Fisher discriminant performs poorly due to diverging spectra and they propose to use the independence rule to overcome the problem. We first demonstrate that even...
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作者：Johnstone, Iain M.
作者单位：Stanford University
摘要：Let A and B be independent, central Wishart matrices in p variables with common covariance and having in and n degrees of freedom, respectively. The distribution of the largest eigenvalue of (A + B)(-1) B has numerous applications in multivariate statistics, but is difficult to calculate exactly. Suppose that in and n grow in proportion to p. We show that after centering and scaling, the distribution is approximated to second-order, O(p(-2/3)), by the Tracy-Widom law. The results are obtained ...
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作者：Chamandy, N.; Worsley, K. J.; Taylor, J.; Gosselin, F.
作者单位：McGill University; Alphabet Inc.; Google Incorporated; University of Chicago; Stanford University; Universite de Montreal
摘要：Local increases in the mean of a random field are detected (conservatively) by thresholding a field of test statistics at a level u chosen to control the tail probability or p-value of its maximum. This p-value is approximated by the expected Euler characteristic (EC) of the excursion set of the test statistic field above u, denoted E phi (A(u)). Under isotropy, one can use the expansion E phi(A(u)) = Sigma(k) V(k rho k()u), where V-k is an intrinsic volume of the parameter space and rho(k) is...
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作者：Cheng, Guang; Kosorok, Michael R.
作者单位：Duke University; University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution. The first order validity of this procedure established by Lee, Kosorok and Fine in [J. American Statist. Assoc. 100 (2005) 960969] is extended to second-order validity in the setting where the infinite-dimensional nuisance parameter achieves the parametric rate. Specifically, we obtain higher order estimates of the maximum profile like...
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作者：Grama, Ion; Spokoiny, Vladimir
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We use the fitted Pareto law to construct an accompanying approximation of the excess distribution function. A selection rule of the location of the excess distribution function is proposed based on a stagewise lack-of-fit testing procedure. Our main result is an oracle type inequality for the Kullback-Leibler loss.
