The Annals of Statistics

最新文章

• The Lukacs-Olkin-Rubin characterization of Wishart distributions on symmetric cones AI翻译
  作者：Casalis, M; Letac, G
  摘要：We characterize the Wishart distributions on a symmetric cone C. If C = (0, +infinity), this has been done by Lukacs in 1955. If C is the cone of positive definite symmetric matrices, this has been done by Olkin and Rubin in 1962. We both shorten and extend the Olkin-Rubin proof (sometimes obscure) by using three modern ideas: (i) try to avoid artificial coordinates in differential geometry; (ii) the variance function of a natural exponential family F characterizes F; (iii) symmetric matrices ...
• Convergence properties of the Gibbs sampler for perturbations of Gaussians AI翻译
  作者：Amit, Y
  摘要：The exact second eigenvalue of the Markov operator of the Gibbs sampler with random sweep strategy for Gaussian densities is calculated, A comparison lemma yields an upper hound on the second eigenvalue for bounded perturbations of Gaussians which is a significant improvement over previous bounds. For two-block Gibbs sampler algorithms with a perturbation of the form chi(g(1)(x((1))) + g(2)(x((2)))) the derivative of the second eigenvalue of the algorithm is calculated exactly at chi = 0, in t...
• Asymptotics of some estimators and sequential residual empiricals in nonlinear time series AI翻译
  作者：Koul, HL
  摘要：This paper establishes the asymptotic uniform linearity of M- and R-scores in a family of nonlinear time series and regression models. It also gives an asymptotic expansion of the standardized sequential residual empirical process in these models. These results are, in turn, used to obtain the asymptotic normality of certain classes of M-, R- and minimum distance estimators of the underlying parameters. The classes of estimators considered include analogs of Hodges-Lehmann, Huber and LAD (leas...
• Estimation with prescribed proportional accuracy for a two-parameter exponential family of distributions AI翻译
  作者：Bose, A; Boukai, B
  作者单位：Purdue University System; Purdue University; Purdue University in Indianapolis
  摘要：We propose a sequential procedure for estimating with prescribed proportional accuracy one parameter in a class of two-parameter exponential family of distributions, We study the properties of the resulting stopping time and provide second-order analysis of the coverage probability associated with it by using Edgeworth expansion.
• Complete order statistics in parametric models AI翻译
  作者：Mattner, L
  摘要：For a given statistical model P it may happen that the order statistic is complete for each IID model based on P. After reviewing known relevant results for large nonparametric models and pointing out generalizations to small nonparametric models, we essentially prove that this happens generically even in smooth parametric models. As a consequence it may be argued that any statistic depending symmetrically on the observations can be regarded as an optimal unbiased estimator of its expectation....
• Some inequalities for symmetric convex sets with applications AI翻译
  作者：Anderson, TW
  摘要：Under appropriate conditions the probability of a convex symmetric set decreases as the spread or scatter of the distribution increases. This paper studies the conditions when the random vector has a symmetric unimodal distribution.
• Quasi-likelihood models and optimal inference AI翻译
  作者：Wefelmeyer, W
  摘要：Consider an ergodic Markov chain on the real line, with parametric models for the conditional mean and variance of the transition distribution. Such a setting is an instance of a quasi-likelihood model. The customary estimator for the parameter is the maximum quasi-likelihood estimator. It is not efficient, but as good as the best estimator that ignores the parametric model for the conditional variance. We construct two efficient estimators. One is a convex combination of solutions of two esti...
• Local likelihood density estimation AI翻译
  作者：Loader, CR
  摘要：Local likelihood was introduced by Tibshirani and Hastie as a method of smoothing by local polynomials in non-Gaussian regression models. In this paper an extension of these methods to density estimation is discussed, and comparison with other methods of density estimation presented. The local likelihood method has particularly strong advantages over kernel methods when estimating tails of densities and in multivariate settings. Suppose constraints are incorporated in a simple manner. Asymptot...
• Optimal rates of convergence of empirical Bayes tests for the continuous one-parameter exponential family AI翻译
  作者：Karunamuni, RJ
  摘要：The empirical Bayes linear loss two-action problem in the continuous one-parameter exponential family is studied, Previous results on this problem construct empirical Bayes tests via kernel density estimates, They also obtain upper bounds for the unconditional regret at some prior distribution. In this paper, we discuss the general question of how difficult the above empirical Bayes problem is, and why empirical Bayes rules based on kernel density estimates are useful. Asymptotic minimax-type ...
• Automatic bandwidth choice and confidence intervals in nonparametric regression AI翻译
  作者：Neumann, MH
  摘要：In the present paper we combine the issues of bandwidth choice and construction of confidence intervals in nonparametric regression. Main emphasis is put on fully data-driven methods. We modify the root n-consistent bandwidth selector of Hardle, Hall and Marron such that it is appropriate for heteroscedastic data, and we show how one can optimally choose the bandwidth g of the pilot estimator <(m)over cap(g)>. Then we consider classical confidence intervals based on kernel estimators with data...