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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...
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作者：Butucea, Cristina
作者单位：Universite Paris Nanterre; Sorbonne Universite
摘要：We consider the convolution model where i.i.d. random variables Xi having unknown density f are observed with additive i.i.d. noise, independent of the X's. We assume that the density f belongs to either a Sobolev class or a class of supersmooth functions. The noise distribution is known and its characteristic function decays either polynornially or exponentially asymptotically. We consider the problem of goodness-of-fit testing in the convolution model. We prove upper bounds for the risk of a...
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作者：He, Heping; Severini, Thomas A.
作者单位：Northwestern University; University of Melbourne
摘要：Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order n(-1), where n is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as ((theta) over cap, a), where theta is the maximum likelihood estimator of the parameter theta of the model and a is an ancillary statistic. This condition is very difficult or impossible to verify for many models. However, calculation of the statis...
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作者：Merkl, Franz; Mohammadi, Leila
作者单位：University of Munich; Leiden University; Leiden University Medical Center (LUMC); Leiden University - Excl LUMC
摘要：This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the estimation errors to be large on a scale determined by the inverse cube root of the sample size. As corollaries, we obtain probabilistic bounds for the prediction error in a classification problem. The key to the proof is an entropy estimate. The lower bounds are b...
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作者：Merkouris, T.
作者单位：Statistics Canada
摘要：An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function, the Laplace transform or the probability generating function. This method involves the construction of classes of transform-based martingale estimating functions that fit into the general framework of quasi-likelihood. In the parametric setting of a discrete t...
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作者：Chatterjee, Sourav
作者单位：University of California System; University of California Berkeley
摘要：The Shenington-Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the one-parameter exponential family with quadratic sufficient statistic. Under bare minimal conditions, we establish the root N-consistency of the maximum pseudolikelihood estimate of the natural parameter in this family, even at critical temperatures. Since very little is known about the low and critical temperature regimes of these extre...
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作者：Wellner, Jon A.; Zhang, Ying
作者单位：University of Washington; University of Washington Seattle; University of Iowa
摘要：We consider estimation in a particular semiparametric regression model for the mean of a counting process with panel count data. The basic model assumption is that the conditional mean function of the counting process is of the form E{N(t)vertical bar Z} = exp(beta(T)(0)Z)Lambda(0)(t) where Z is a vector of covariates and Lambda(0) is the baseline mean function. The panel count observation scheme involves observation of the counting process N for an individual at a random number K of random ti...
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作者：Bartroff, Jay
作者单位：University of Southern California
摘要：A family of variable stage size multistage tests of simple hypotheses is described, based on efficient multistage sampling procedures. Using a loss function that is a linear combination of sampling costs and error probabilities, these tests are shown to minimize the integrated risk to second order as the costs per stage and per observation approach zero. A numerical study shows significant improvement over group sequential tests in a binomial testing problem.
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作者：Brown, Lawrence D.; Levine, M.
作者单位：University of Pennsylvania; Purdue University System; Purdue University
摘要：Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for suitable asymptotic formulations our estimators achieve the minimax rate.
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作者：Wang, Haonan; Marron, J. S.
作者单位：Colorado State University System; Colorado State University Fort Collins; University of North Carolina; University of North Carolina Chapel Hill
摘要：Object oriented data analysis is the statistical analysis of populations of complex objects. In the special case of functional data analysis, these data objects are curves, where standard Euclidean approaches, such as principal component analysis, have been very successful. Recent developments in medical image analysis motivate the statistical analysis of populations of more complex data objects which are elements of mildly non-Euclidean spaces, such as Lie groups and symmetric spaces, or of s...
