The Annals of Statistics

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• Cone order association and stochastic cone ordering with applications to order-restricted testing AI翻译
  作者：Cohen, A; Sackrowitz, HB
  摘要：Cohen, Sackrowitz and Samuel-Cahn introduced the notion of cone: order association and established a necessary and sufficient condition for a normal random vector to be cone order associated (COA). In this paper we provide the following: (1) a necessary and sufficient condition for a multinomial distribution to be COA when the cone is a pairwise contrast cone; (2) a relationship between COA and regular association; (5) a notion of stochastic cone ordering (SCO) of random vectors along with two...
• On the asymptotic distribution of a general measure of monotone dependence AI翻译
  作者：Cifarelli, DM; Conti, PL; Regazzini, E
  作者单位：Consiglio Nazionale delle Ricerche (CNR); Sapienza University Rome
  摘要：In this paper the asymptotic normality of a class of statistics, including Gini's index of cograduation and Spearman's rank correlation coefficient, is proved. The asymptotic normality is stated under a large class of alternatives including the bivariate distributions corresponding to a condition of lack of association introduced in Section 3. The problems of testing the hypothesis of lack of association and of constructing confidence intervals for the population index of cograduation are also...
• Rates of convergence of the Hastings and Metropolis algorithms AI翻译
  作者：Mengersen, KL; Tweedie, RL
  作者单位：Colorado State University System; Colorado State University Fort Collins
  摘要：We apply recent results in Markov chain theory to Hastings and Metropolis algorithms with either independent or symmetric candidate distributions, and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi. In the independence case (in R(k)) these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi; in the symmetric case (in R only) we show geomet...
• On nonparametric estimation of intercept and slope distributions in random coefficient regression AI翻译
  作者：Beran, R; Feuerverger, A; Hall, P
  作者单位：University of Toronto; Australian National University
  摘要：An experiment records stimulus and response for a random sample of cases. The relationship between response and stimulus is thought to be linear, the values of the slope and intercept varying by case. From such data, we construct a consistent, asymptotically normal, nonparametric estimator for the joint density of the slope and intercept. Our methodology incorporates the radial projection-slice theorem for the Radon transform, a technique for locally linear nonparametric regression and a taper...
• Universal Gaussian approximations under random censorship AI翻译
  作者：Csorgo, S
  摘要：Universal Gaussian approximations are established for empirical cu mulative hazard and product-limit processes under random censorship. They hold uniformly up to some large order statistics in the sample, with the approximation rates depending on the order of these statistics, and require no assumptions on the censoring mechanism. Weak convergence results and laws of the iterated logarithm follow on the whole line if the respective processes are stopped at certain large order statistics, depen...
• Reducing multidimensional two-sample data to one-dimensional interpoint comparisons AI翻译
  作者：Maa, JF; Pearl, DK; Bartoszynski, R
  作者单位：University System of Ohio; Ohio State University
  摘要：The most popular technique for reducing the dimensionality in comparing two multidimensional samples of X similar to F and Y similar to G is to analyze distributions of interpoint comparisons based on a univariate function h (e.g. the interpoint distances). We provide a theoretical foundation for this technique, by showing that having both i) the equality of the distributions of within sample comparisons (h(X(1),X(2)) =(L) h(Y-1,Y-2)) and ii) the equality of these with the distribution of betw...
• Asymptotics of least-squares estimators for constrained nonlinear regression AI翻译
  作者：Wang, JD
  摘要：This paper is devoted do studying the asymptotic behavior of LS-estimators in constrained nonlinear regression problems. Here the constraints are given by nonlinear equalities and inequalities. Thus this is a very general setting. Essentially this kind of estimation problem is a stochastic optimization problem. So we make use of methods in optimization to overcome the difficulty caused by nonlinearity in the regression model and given constraints.
• On bootstrap accuracy with censored data AI翻译
  作者：Chen, K; Lo, SH
  作者单位：Columbia University
  摘要：In survival analysis with censored data, we consider three closely related survival function estimators: the Kaplan-Meier, Nelson and moment estimators. We derive the Edgeworth expansions for these three estimators with Studentization. Edgeworth expansions for the corresponding bootstrap statistics are also given. It is found that the bootstrap approximation is better than the normal approximation for the Studentized Kaplan-Meier and Nelson estimators, but not so for the Studentized moment est...
• Asymptotically uniformly most powerful tests in parametric and semiparametric models AI翻译
  作者：Choi, SS; Hall, WJ; Schick, A
  作者单位：University of Rochester; State University of New York (SUNY) System; Binghamton University, SUNY
  摘要：Tests of hypotheses about finite-dimensional parameters in a semiparametric model are studied from Pitman's moving alternative (or local) approach using Le Cam's local asymptotic normality concept. For the case of a real parameter being tested, asymptotically uniformly most powerful (AUMP) tests are characterized for one-sided hypotheses, and AUMP unbiased tests for two-sided ones. An asymptotic invariance principle is introduced for multidimensional hypotheses, and AUMP invariant tests are ch...
• Efficient maximum likelihood estimation in semiparametric mixture models AI翻译
  作者：VanderVaart, A
  摘要：We consider maximum likelihood estimation in several examples of semiparametric mixture models, including the exponential frailty model and the errors-in-variables model. The observations consist of a sample of size n from the mixture density integral p(theta)(x\z)d eta(z). The mixing distribution is completely unknown. We show that the first component <(theta(n))over tilde> of the joint maximum likelihood estimator (<(theta(n))over tilde>, <(eta(n))over tilde>) is asymptotically normal and as...