The Annals of Statistics

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• The consistency of the BIC Markov order estimator AI翻译
  作者：Csiszár, I; Shields, PC
  作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences; University System of Ohio; University of Toledo
  摘要：The Bayesian Information Criterion (BIC) estimates the order of a Markov chain (with finite alphabet A) from observation of a sample path x(1), x(2), ..., x(n), as that value k = (k) over cap that minimizes the sum of the negative logarithm of the kth order maximum likelihood and the penalty term \A\(k)(\A\-1)/2. We show that (k) over cap equals the correct order of the chain, eventually almost surely as it --> infinity, thereby strengthening earlier consistency results that assumed an apriori...
• Constrained D- and D1-optimal designs for polynomial regression AI翻译
  作者：Dette, H; Franke, T
  作者单位：Ruhr University Bochum
  摘要：In the common polynomial regression model of degree m we consider the problem of determining the D- and D-1-optimal designs subject to certain constraints for the D-1-efficiencies in the models of degree m - j, m - j + 1..... m + k(m > j greater than or equal to 0, k greater than or equal to 0 given). We present a complete solution of these problems, which on the one hand allow a fast computation of the constrained optimal designs and on the other hand give an answer to the question of the exi...
• Maximum likelihood estimation of smooth monotone and unimodal densities AI翻译
  作者：Eggermont, PPB; LaRiccia, VN
  作者单位：University of Delaware
  摘要：We study the nonparametric estimation of univariate monotone and unimodal densities using the maximum smoothed likelihood approach. The monotone estimator is the derivative of the least concave majorant of the distribution corresponding to a kernel estimator. We prove that the mapping on distributions Phi with density phi, phi bar right arrow the derivative of the least concave majorant of Phi, is a contraction in all L-P norms (1 less than or equal to p less than or equal to infinity), and so...
• Confidence bands in generalized linear models AI翻译
  作者：Sun, JY; Loader, C; McCormick, WP
  作者单位：University System of Ohio; Case Western Reserve University; AT&T; Alcatel-Lucent; Lucent Technologies; University System of Georgia; University of Georgia
  摘要：Generalized linear models (GLM) include many useful models. This paper studies simultaneous confidence regions for the mean response function in these models. The coverage probabilities of these regions are related to tail probabilities of maxima of Gaussian random fields, asymptotically, and hence, the so-called tube formula is applicable without any modification. However, in the generalized linear models, the errors are often nonadditive and non-Gaussian and may be discrete. This poses a cha...
• Additive logistic regression: A statistical view of boosting - Discussion AI翻译
  作者：Buja, A
  作者单位：AT&T
• Additive logistic regression: A statistical view of boosting - Rejoinder AI翻译
  作者：Friedman, J; Hastie, T; Tibshirani, R
  作者单位：Stanford University
• On an empiricial Bayes test for a normal mean AI翻译
  作者：Liang, TC
  作者单位：Wayne State University
  摘要：We exhibit an empirical Bayes test delta(n)(*) for the normal mean testing problem using a linear error loss. Under the condition that the critical point of a Bayes test is within some known compact interval, delta(n)(*) is shown to be asymptotically optimal and its associated regret Bayes risk converges to zero at a rate O(n(-1)(ln n)(1.5)), where n is the number of past experiences available when the current component decision problem is considered. Under the same condition this rate is fast...
• On the asymptotic distribution theory of a class of consistent estimators of a distribution satisfying a uniform stochastic ordering constraint AI翻译
  作者：Arcones, MA; Samaniego, FJ
  作者单位：State University of New York (SUNY) System; Binghamton University, SUNY; University of California System; University of California Davis
  摘要：We identify the asymptotic behavior of the estimators proposed by Rojo and Samaniego and Mukejee of a distribution F assumed to be uniformly stochastically smaller than a known baseline distribution G. We show that these estimators are root n-convergent to a limit distribution with mean squared error smaller than or equal to the mean squared error of the empirical survival function. By examining the mean squared error of the limit distribution, we are able to identify the optimal estimator wit...
• Asymptotically efficient strategies for a stochastic scheduling problem with order constraints AI翻译
  作者：Fuh, CD; Hu, IC
  作者单位：Academia Sinica - Taiwan; Hong Kong University of Science & Technology
  摘要：Motivated by an application in computerized adaptive tests, we consider the following sequential design problem. There are J jobs to be processed according to a predetermined order. A single machine is available to process these J jobs. Each job under processing evolves stochastically as a Markov chain and earns rewards as it is processed, not otherwise. The Markov chain has transition probabilities parameterized by an unknown parameter theta. The objective is to determine how long each job sh...
• Sequential confidence regions for maximum likelihood estimates AI翻译
  作者：Dmitrienko, A; Govindarajulu, Z
  作者单位：Eli Lilly; Lilly Research Laboratories; University of Kentucky
  摘要：The goal of this paper is ti,develop a general framework for constructing sequential fixed size confidence regions based on maximum likelihood estimates. Asymptotic properties of the sequential procedure for setting up the confidence regions are analyzed under very broad assumptions on the underlying parametric model. It is shown that the proposed sequential procedure is asymptotically optimal in the sense that it approximates the optimal fixed-sample size procedure. It is further shown that t...