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作者：Pensky, Marianna; Sapatinas, Theofanis
作者单位：State University System of Florida; University of Central Florida; University of Cyprus
摘要：Using the asymptotical minimax framework, we examine convergence rates equivalency between a continuous functional deconvolution model and its real-life discrete counterpart over a wide range of Besov balls and for the L-2-risk. For this purpose, all possible models are divided into three groups. For the models in the first group, which we call uniform, the convergence rates in the discrete and the continuous models coincide no matter what the sampling scheme is chosen, and hence the replaceme...
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作者：Ravikumar, Pradeep; Wainwright, Martin J.; Lafferty, John D.
作者单位：University of California System; University of California Berkeley; Carnegie Mellon University; Carnegie Mellon University
摘要：We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on l(1)-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an l(1)-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n. Our main results pr...
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作者：Lahiri, S. N.
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：In this paper, we derive valid Edgeworth expansions for studentized versions of a large class of statistics when the data are generated by a strongly mixing process. Under dependence, the asymptotic variance of such a statistic is given by an infinite series of lag-covariances, and therefore, studentizing factors (i.e., estimators of the asymptotic standard error) typically involve an increasing number, say, l of lag-covariance estimators, which are themselves quadratic functions of the observ...
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作者：Polunchenko, Aleksey S.; Tartakovsky, Alexander G.
作者单位：University of Southern California
摘要：In 1985, for detecting a change in distribution, Pollak introduced a specific minimax performance metric and a randomized version of the Shiryaev-Roberts procedure where the zero initial condition is replaced by a random variable sampled from the quasi-stationary distribution of the Shiryaev-Roberts statistic. Pollak proved that this procedure is third-order asymptotically optimal as the mean time to false alarm becomes large. The question of whether Pollak's procedure is strictly minimax for ...
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作者：Rosenbaum, Mathieu; Tsybakov, Alexandre B.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Institut Polytechnique de Paris; ENSAE Paris; Sorbonne Universite
摘要：We consider the model y = X theta* + xi, Z = X + Xi, where the random vector y is an element of R-n and the random n x p matrix Z are observed, the n x p matrix X is unknown, Xi is an n x p random noise matrix, xi is an element of R-n is a noise independent of Xi, and theta* is a vector of unknown parameters to be estimated. The matrix uncertainty is in the fact that X is observed with additive error. For dimensions p that can be much larger than the sample size n, we consider the estimation o...
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作者：Fuh, Cheng-Der
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作者：Kuelbs, Jim; Vidyashankar, Anand N.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Cornell University
摘要：In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve situations in which (i) the number of parameters increase with the sample size (that is, allowed to be random) and (ii) there is a possibility of missing data. Under a variety of tail conditions on the components of the data, we provide precise conditions for th...
