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作者：Dette, Holger; Schorning, Kirsten
作者单位：Ruhr University Bochum
摘要：In a recent paper Yang and Stufken [Ann. Statist. 40 (2012a) 1665-1685] gave sufficient conditions for complete classes of designs for nonlinear regression models. In this note we demonstrate that there is an alternative way to validate this result. Our main argument utilizes the fact that boundary points of moment spaces generated by Chebyshev systems possess unique representations.
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作者：Jacod, Jean; Rosenbaum, Mathieu
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：We consider a multidimensional Ito semimartingale regularly sampled on [0, t] at high frequency 1/Delta(n), with Delta(n) going to zero. The goal of this paper is to provide an estimator for the integral over [0, t] of a given function of the volatility matrix. To approximate the integral, we simply use a Riemann sum based on local estimators of the pointwise volatility. We show that although the accuracy of the pointwise estimation is at most Delta(1/4)(n), this procedure reaches the parametr...
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作者：Suzuki, Taiji; Sugiyama, Masashi
作者单位：University of Tokyo; Institute of Science Tokyo; Tokyo Institute of Technology
摘要：We investigate the learning rate of multiple kernel learning (MKL) with l(1) and elastic-net regularizations. The elastic-net regularization is a composition of an l(1)-regularizer for inducing the sparsity and an l(2)-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large, but the number of nonzero components of the ground truth is relatively small, and show sharper convergence rates than the learning rates have ever shown for both ...
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作者：Masuda, Hiroki
作者单位：Kyushu University
摘要：This paper investigates the Gaussian quasi-likelihood estimation of an exponentially ergodic multidimensional Markov process, which is expressed as a solution to a Levy driven stochastic differential equation whose coefficients are known except for the finite-dimensional parameters to be estimated, where the diffusion coefficient may be degenerate or even null. We suppose that the process is discretely observed under the rapidly increasing experimental design with step size h(n). By means of t...
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作者：Rinaldo, Alessandro; Petrovic, Sonja; Fienberg, Stephen E.
作者单位：Carnegie Mellon University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Carnegie Mellon University
摘要：We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the beta-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based on the polytope of degree sequences, for the existence of the maximum likelihood estimator (MLE) of the model parameters. We characterize in a combinatorial fashion sample points leading to a nonexistent MLE, and nonestimability of the probability parameters u...
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作者：Birnbaum, Aharon; Johnstone, Iain M.; Nadler, Boaz; Paul, Debashis
作者单位：Hebrew University of Jerusalem; Stanford University; Weizmann Institute of Science; University of California System; University of California Davis
摘要：We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the l(2) loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the risk points to the existence of different regimes of sparsity of the eigenvectors. We also propose a n...
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作者：Chatterjee, A.; Lahiri, S. N.
作者单位：Indian Statistical Institute; Indian Statistical Institute Delhi; North Carolina State University
摘要：Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] proposed the Adaptive LASSO (ALASSO) method for simultaneous variable selection and estimation of the regression parameters, and established its oracle property. In this paper, we investigate the rate of convergence of the ALASSO estimator to the oracle distribution when the dimension of the regression parameters may grow to infinity with the sample size. It is shown that the rate critically depends on the choices of the penalty parameter and...
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作者：Li, Chenxu
作者单位：Peking University
摘要：This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and accompanied by an algorithm containing only basic and explicit calculations for delivering any arbitrary order of the expansion. The likelihood function is thus approximated explicitly and employed in statistical estimation. The performance of our method is demonstra...
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作者：Miller, Jeffrey W.; Harrison, Matthew T.
作者单位：Brown University
摘要：The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this distribution, many approximate methods have been developed. We will show that by exploiting certain symmetries, exact sampling and counting is in fact possible in many nontrivial real-world cases. We illustrate with real datasets including ecological co-occurrence...
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作者：Efromovich, Sam
作者单位：University of Texas System; University of Texas Dallas
摘要：The paper is devoted to the problem of estimation of a univariate component in a heteroscedastic nonparametric multiple regression under the mean integrated squared error (MISE) criteria. The aim is to understand how the scale function should be used for estimation of the univariate component. It is known that the scale function does not affect the rate of the MISE convergence, and as a result sharp constants are explored. The paper begins with developing a sharp-minimax theory for a pivotal m...
