Kernel Estimation of Rate Function for Recurrent Event Data

Abstract.  Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce a curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.     

The analysis of incomplete data using stochastic covariates

In the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV-1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour-bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumours.     

On Rates of Convergence for Bayesian Density Estimation

Abstract.  We consider the problem of estimating a compactly supported density taking a Bayesian nonparametric approach. We define a Dirichlet mixture prior that, while selecting piecewise constant densities, has full support on the Hellinger metric space of all commonly dominated probability measures on a known bounded interval. We derive pointwise rates of convergence for the posterior expected density by studying the speed at which the posterior mass accumulates on shrinking Hellinger neighbourhoods of the sampling density. If the data are sampled from a strictly positive, α -Hölderian density, with α  ∈ ( 0,1] , then the optimal convergence rate n^{− α / (2 α +1)} is obtained up to a logarithmic factor. Smoothing histograms by polygons, a continuous piecewise linear estimator is obtained that for twice continuously differentiable, strictly positive densities satisfying boundary conditions attains a rate comparable up to a logarithmic factor to the convergence rate n ^−4/5 for integrated mean squared error of kernel type density estimators.     

On an adaptive version of the Metropolis–Hastings algorithm with independent proposal distribution

In this paper, we present a general formulation of an algorithm, the adaptive independent chain (AIC), that was introduced in a special context in Gåsemyr et al . [ Methodol. Comput. Appl. Probab. 3 (2001)]. The algorithm aims at producing samples from a specific target distribution Π, and is an adaptive, non-Markovian version of the Metropolis–Hastings independent chain. A certain parametric class of possible proposal distributions is fixed, and the parameters of the proposal distribution are updated periodically on the basis of the recent history of the chain, thereby obtaining proposals that get ever closer to Π. We show that under certain conditions, the algorithm produces an exact sample from Π in a finite number of iterations, and hence that it converges to Π. We also present another adaptive algorithm, the componentwise adaptive independent chain (CAIC), which may be an alternative in particular in high dimensions. The CAIC may be regarded as an adaptive approximation to the Gibbs sampler updating parametric approximations to the conditionals of Π.     

教育行动研究与在职外语教师的专业发展

教育行动研究作为一种解决现实课堂教学问题的实践方法和特殊的教师教育方法正受到越来越多的国内外教育研究者的关注。它倡导教师即研究者通过对自己课堂中的教学现象进行考察和研究并从中获取知识,改进教学质量。教育行动研究与教师专业发展密切相关。教育行动研究可以改进教学质量,提高教学水平,帮助在职教师重建知识体系,促使教师向专家型教师转化,是在职外语教师专业发展的可行的、有效的途径。     

佛山目标产业体系的抉择与逼近──兼论利用外资优化佛山产业结构

分析了区域裂变后的佛山产业体系发展的现状，并结合佛山未来的经济发展战略，勾勒出佛山目标产业体系，同时提出了以外资的利用作为优化佛山产业体系动力源的对策思路。     

世纪之交屈原研究的回顾和展望──'99岳阳两湖屈原与楚文化研讨会综述

综述了参与’99湖南岳阳两湖屈原与楚文化学术研讨会的专家学者的主要研究成果,介绍了有关世纪之交屈原研究的回顾与展望方面的成果。     

教育国际化及高校外事工作的目标定位

从经济全球化、国家软实力建设、教育经济、校本建设四个维度,阐述我国教育国际化及高校外事工作所承载的社会发展意义与担负的历史使命,并将上述四个维度作为参照系,确定了高校外事工作应有的目标取向与定位。     

隆线溞(Daphnia carinata king)的呼吸代谢测定

本文用Winkler法测定隆线溞(Caphnia carinata king)不同龄期个体的耗氧量及二幼龄个体在不同温度下的耗氧量。测得幼龄与成龄两阶段,其耗氧量分别以4.88×10~(-2)与1.695×10~(-1)的速率随体重增加而增大,耗氧率则分别随体重的增加而逐渐降低;在常温下,隆线溞耗氧量Y与温度X呈Y=3.69×10~(-3)×1.07~x的指数函数关系,由此得到,17℃—19℃是隆线搔生长速率快而耗氧量较小的最适人工培养温度。