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作者：Bickel, Peter J.; Levina, Elizaveta
作者单位：University of California System; University of California Berkeley; University of Michigan System; University of Michigan
摘要：This paper considers estimating a covariance matrix of p variables from n observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these estimates are consistent in the operator norm as long as (log p)/n -> 0, and obtain explicit rates. The results are uniform over some fairly natural well-conditioned families of covariance matrices. We also introduce an analogue of the Gaussian white noise model and ...
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作者：Chen, Songnian; Zhou, Lingzhi
作者单位：Hong Kong University of Science & Technology
摘要：Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661-1690] considered the estimation of the risk function psi(x) in the proportional hazards model. Their proposed estimator is based on integrating the estimated derivative function obtained through a local version of the partial likelihood. They proved the large sample properties of the derivative function, but the large sample properties of the estimator for the risk function itself were not established. In this paper, we consider direct estima...
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作者：Genest, Christian; Quessy, Jean-Francois; Remillard, Bruno
作者单位：Laval University; University of Quebec; University of Quebec Trois Rivieres; Universite de Montreal; HEC Montreal
摘要：Deheuvels [J. Multivariate Anal. 11 (1981) 102-113] and Genest and Remillard [Test 13 (2004) 335-369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent Cramer-von Mises statistics derived from a Mobius decomposition of the empirical copula process. A result on the large-sample behavior of this process under contiguous sequences of alternatives is used here to give a representation of the limiting distribution of such tes...
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作者：Hall, Peter; Horowitz, Joel L.
作者单位：University of Melbourne; Northwestern University
摘要：In functional linear regression, the slope parameter is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an ill-posed problem and has points of contact with a range of methodologies, including statistical smoothing and deconvolution. The standard approach to estimating the slope function is based explicitly on functional principal components analysis and, consequently, on spectral decomposition in terms of ei...
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作者：Karlsen, Hans Arnfinn; Myklebust, Terje; Tjostheim, Dag
作者单位：University of Bergen
摘要：We derive an asymptotic theory of nonparametric estimation for a time series regression model Z(t) = f (X-t) + W-t, where {X-t) and {Z(t)} are observed nonstationary processes and {W-t} is an unobserved stationary process. In econometrics, this can be interpreted as a nonlinear cointegration type relationship, but we believe that our results are of wider interest. The class of nonstationary processes allowed for {Xt} is a subclass of the class of null recurrent Markov chains. This subclass con...
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作者：Hall, Peter; Ma, Yanyuan
作者单位：University of Melbourne; Texas A&M University System; Texas A&M University College Station
摘要：A low-degree polynomial model for a response curve is used commonly in practice. It generally incorporates a linear or quadratic function of the covariate. In this paper we suggest methods for testing the goodness of fit of a general polynomial model when there are errors in the covariates. There, the true covariates are not directly observed, and conventional bootstrap methods for testing are not applicable. We develop a new approach, in which deconvolution methods are used to estimate the di...
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作者：Carter, Andrew V.
作者单位：University of California System; University of California Santa Barbara
摘要：Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown nuisance parameter. We establish an asymptotic approximation to the nonparametric regression experiment when the value of the variance is an additional parameter to be estimated or tested. This asymptotically equivalent experiment has two components: the first ...
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作者：Chi, Zhiyi
作者单位：University of Connecticut
摘要：The False Discovery Rate (FDR) paradigm aims to attain certain control on Type I errors with relatively high power for multiple hypothesis testing. The Benjamini-Hochberg (BH) procedure is a well-known FDR controlling procedure. Under a random effects model, we show that, in general, unlike the FDR, the positive FDR (pFDR) of the BH procedure cannot be controlled at an arbitrarily low level due to the limited evidence provided by the observations to separate false and true nulls. This results ...
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作者：Csoergo, Miklos; Szyszkowicz, Barbara; Wang, Lihong
作者单位：Carleton University; Nanjing University
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作者：Abramovich, Felix; Grinshtein, Vadim; Pensky, Marianna
作者单位：Tel Aviv University; Open University Israel; State University System of Florida; University of Central Florida
摘要：We consider a problem of recovering a high-dimensional vector mu observed in white noise, where the unknown vector g is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family of l(0)-type penalties. The penalties are associated with various choices of the prior distributions pi(n)(center dot) on the number of nonzero entries of mu and, hence, are easy to interpret. The resulting Bayesian estimators lead to a general thresholding rule wh...
