-
作者：Drton, Mathias; Massam, Helene; Olkin, Ingram
作者单位：University of Chicago; York University - Canada; Stanford University
摘要：For a random matrix following a Wishart distribution, we derive formulas for the expectation and the covariance matrix of compound matrices. The compound matrix of order m is populated by all m x m-minors of the Wishart matrix. Our results yield first and second moments of the minors of the sample covariance matrix for multivariate normal observations. This work is motivated by the fact that such minors arise in the expression of constraints on the covariance matrix in many classical multivari...
-
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...
-
作者：Bellon, Alexandre; Didier, Gustavo
作者单位：Duke University; Tulane University
摘要：In this paper we provide a provably convergent algorithm for the multi-variate Gaussian Maximum Likelihood version of the Behrens-Fisher Problem. Our work builds upon a formulation of the log-likelihood function proposed by Buot and Richards [5]. Instead of focusing on the first order optimality conditions, the algorithm aims directly for the maximization of the log-likelihood function itself to achieve a global solution. Convergence proof and complexity estimates are provided for the algorith...
-
作者：Owen, Art B.
作者单位：Stanford University
摘要：We consider the problem of computing an approximation to the integral I = integral([0, 1])d f (x) dx. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of O(n(-1/2)) from n independent random function evaluations. By contrast, quasi-Monte Carlo (QMC) sampling using carefully equispaced evaluation points can attain the rate O(n(-1+epsilon)) for any epsilon > 0 and randomized QMC (RQMC) can attain the RMSE O(n(-3/2+epsilon)), both under mild conditions on f. Classical ...
-
作者：Cai, T. Tony; Wang, Lie
作者单位：University of Pennsylvania
摘要：We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences of the observations. We show that the variance function estimator is nearly optimally adaptive to the smoothness of both the mean and variance functions. The estimator is shown to achieve the optimal adaptive rate of convergence under the pointwise squared ...
-
作者：Cuesta-Albertos, Juan A.; Matran, Carlos; Mayo-Iscar, Agustin
作者单位：Universidad de Cantabria; Universidad de Valladolid
摘要：Robust estimators of location and dispersion are Often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data Outside an ellipsoid based in the associated Mahalanobis distance. Here we analyze some one (or k)-step Maximum Likelihood Estimators computed on a subsample obtained with Such a procedure. We introduce different models which arise naturally from the ways in which the discarded data can be treated, leading to truncated or censo...
-
作者：Jiang, Wenxin; Tanner, Martin A.
作者单位：Northwestern University
摘要：In the popular approach of Bayesian variable selection (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with I Gibbs posterior originating in statistical mechanics. The Gibbs posterior is constructed from a risk function of practical interest (Such as the classification error) and aims at minimizing a risk function without modeling the data probabilistically. This can ...
-
作者：Hall, Peter; Lahiri, Soumendra N.
作者单位：University of Melbourne; Texas A&M University System; Texas A&M University College Station
摘要：When using the bootstrap in the presence of measurement error, we must first estimate the target distribution function; we cannot directly resample since we don not have a sample from the target. These and other considerations motivate the development of estimators of distributions, and of related quantities such as moments and quantiles, in errors-in-variables settings. We show that such estimators have curious and unexpected properties. For example, if the distributions of the variable of in...
-
作者：Robinson, P. M.
作者单位：University of London; London School Economics & Political Science
摘要：Moving from univariate to bivariate jointly dependent long-memory time series introduces a phase parameter (gamma), at the frequency of principal interest. zeros for short-memory series gamma = 0 automatically. The latter case has also been stressed under long memory, along with the fractional differencing case gamma = (delta(2) - delta(1))pi/2, where delta(1), delta(2) are the memory parameters of the two series. We develop time domain conditions under which these are and are not relevant, an...
-
作者：Leonenko, Nikolai; Pronzat, Luc; Savani, Vippal
作者单位：Cardiff University; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur
摘要：A class of estimators of the Renyi and Tsallis entropies of an unknown distribution f in R-m is presented. These estimators are based on the kth nearest-neighbor distances computed from a sample of N i.i.d. vectors with distribution f. We show that entropies of any order q, including Shannon's entropy, can be estimated consistently with minimal assumptions on f. Moreover, we show that it is straightforward to extend the nearest-neighbor method to estimate the statistical distance between two d...
