The Annals of Statistics

最新文章

• Local extremes, runs, strings and multiresolution - Rejoinder AI翻译
  作者：Davies, PL; Kovac, A
  作者单位：University of Duisburg Essen
• Local extremes, runs, strings and multiresolution - Discussion AI翻译
  作者：Marron, JS
  作者单位：University of North Carolina; University of North Carolina Chapel Hill
• Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities AI翻译
  作者：Ghosal, S; Van der Vaart, AW
  作者单位：University of Minnesota System; University of Minnesota Twin Cities; Vrije Universiteit Amsterdam
  摘要：We study the rates of convergence of the maximum likelihood estimator (MLE) and posterior distribution in density estimation problems, where the densities are location or location-scale mixtures of normal distributions with the scale parameter lying between two positive numbers. The true density is also assumed to lie in this class with the true mixing distribution either compactly supported or having sub-Gaussian tails. We obtain bounds for Hellinger bracketing entropies for this class, and f...
• Generalized likelihood ratio statistics and Wilks phenomenon AI翻译
  作者：Fan, JQ; Zhang, CM; Zhang, J
  作者单位：Chinese University of Hong Kong; University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Los Angeles
  摘要：Likelihood ratio theory has had tremendous success in parametric inference, due to the fundamental theory of Wilks. Yet, there is no general applicable approach for nonparametric inferences based on function estimation. Maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting. Even if they exist, they are hard to find and can not; be optimal as shown in this paper. We introduce the generalized likelihood statistics to overcome the drawbacks...
• Local extremes, runs, strings and multiresolution - Discussion AI翻译
  作者：Mammen, E; Van de Geer, S
  作者单位：Ruprecht Karls University Heidelberg; Leiden University; Leiden University - Excl LUMC
• Improving on the MLE of a bounded normal mean AI翻译
  作者：Marchand, É; Perron, F
  作者单位：University of New Brunswick; Universite de Montreal
  摘要：We consider the problem of estimating the mean of a p-variate normal distribution with identity covariance matrix when the mean lies in a ball of radius m. It follows from general theory that dominating estimators of the maximum likelihood estimator always exist when the loss is squared error. We provide and describe explicit classes of improvements for all problems (m, p). We show that, for small enough m, a wide class of estimators. including all Bayes estimators with respect to orthogonally...
• Narrow-band analysis of nonstationary processes AI翻译
  作者：Robinson, PM; Marinucci, D
  作者单位：University of London; London School Economics & Political Science
  摘要：The behavior of averaged periodograms and cross-periodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones. The cross-periodogram can involve two nonstationary processes of possibly different orders, or a nonstationary and an asymptotically stationary one. The averaging takes place either over the whole frequency band, or over one that degenerates slowly to ...
• Maximin designs for exponential growth models and heteroscedastic polynomial models AI翻译
  作者：Imhof, LA
  作者单位：Stanford University
  摘要：This paper is concerned with nonsequential optimal designs for a class of nonlinear growth models, which includes the asymptotic regression model. This design problem is intimately related to the problem of finding optimal designs for polynomial regression models with only partially known heteroscedastic structure. In each case, a straightforward application of the usual D-optimality criterion would lead to designs which depend on the unknown underlying parameters. To overcome this undesirable...
• Gaussian estimation of parametric spectral density with unknown pole AI翻译
  作者：Giraitis, L; Hidalgo, J; Robinson, PM
  作者单位：University of London; London School Economics & Political Science
  摘要：We consider a parametric spectral density with power-law behavior about a fractional pole at the unknown frequency omega. The case of known omega, especially omega = 0, is standard in the long memory literature. When omega is unknown, asymptotic distribution theory for estimates of parameters, including the (long) memory parameter, is significantly harder. We study a form of Gaussian estimate. We establish n-consistency of the estimate of omega, and discuss its (non-standard) limiting distribu...
• Multiscale testing of qualitative hypotheses AI翻译
  作者：Dümbgen, L; Spokoiny, VG
  作者单位：University of Lubeck; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
  摘要：Suppose that one observes a process Y on the unit interval, where dY(t) = n(1/2)f(t) dt + dW (t) with an unknown function parameter f, given scale parameter n greater than or equal to 1 (sample size) and standard Brownian motion W. We propose two classes of tests of qualitative nonparametric hypotheses about f such as monotonicity or concavity. These tests are asymptotically optimal and adaptive in a certain sense. They are constructed via a new class of multiscale statistics and an extension ...