The Product-Limit Estimate as an Inverse-Probability-Weighted Average

Abstract

For randomly censored data, (Satten, G. A., Datta S. (2001 Satten, G. A. and Datta, S. 2001. The Kaplan–Meier estimator as an inverse-probability-of-censoring weighted average. Amer. Statist. Ass., 55: 207–210. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The Kaplan–Meier estimator as an inverse-probability-of-censoring weighted average. Amer. Statist. Ass. 55:207–210) showed that the Kaplan–Meier estimator (product-limit estimator (PLE)) can be expressed as an inverse-probability-weighted average. In this article, we consider the other two PLEs: the truncation PLE and the censoring-truncation PLE. For the data subject to left-truncation or both left-truncation and right-censoring, it is shown that these two PLEs can be expressed as inverse-probability-weighted averages.     

SOJOURN TIMES IN NON-HOMOGENEOUS QBD PROCESSES WITH PROCESSOR SHARING

We study sojourn times of customers in a processor sharing queue with a service rate that varies over time, depending on the number of customers and on the state of a random environment. An explicit expression is derived for the Laplace–Stieltjes transform of the sojourn time conditional on the state upon arrival and the amount of work brought into the system. Particular attention is paid to the conditional mean sojourn time of a customer as a function of his required amount of work, and we establish the existence of an asymptote as the amount of work tends to infinity. The method of random time change is then extended to include the possibility of a varying service rate. By means of this method, we explain the well-established proportionality between the conditional mean sojourn time and required amount of work in processor sharing queues without random environment. Based on numerical experiments, we propose an approximation for the conditional mean sojourn time. Although first presented for exponentially distributed service requirements, the analysis is shown to extend to phase-type services. The service discipline of discriminatory processor sharing is also shown to fall within the framework.     

Estimation and Welfare Analysis With Large Demand Systems

We develop an approach for estimating individual or household level preferences for a large set of quality-differentiated goods and for constructing Hicksian welfare measures within the demand system framework. Our approach uses a maximum simulated likelihood procedure to recover estimates of the structural parameters and a multistage, Monte Carlo Markov chain algorithm for constructing Hicksian consumer surplus estimates. We illustrate our approach with a recreation dataset consisting of day trips to 62 Mid-Atlantic beaches.     

On some probability distributions associated with random walks

The probability distribution of the total number of games to ruin in a gambler's ruin random walk with initial position n, the probability distribution of the total size of an epidemic starting with n cases and the probability distribution of the number of customers served during a busy period M/M/1 when the service starts with n waiting customers are identical. All these can be easily obtained by using Lagrangian expansions instead of long combinatorial methods. The binomial, trinomial, quadrinomial and polynomial random walks of a particle have been considered with an absorbing barrier at 0 when the particle starts its walks from a point n, and the pgfs. and the probability distributions of the total number of jumps (trials) before absorption at 0 have been obtained. The values for the mean and variance of such walks have also been given.     

Multilevel regression mixture analysis

Summary.  A two-level regression mixture model is discussed and contrasted with the conventional two-level regression model. Simulated and real data shed light on the modelling alternatives. The real data analyses investigate gender differences in mathematics achievement from the US National Education Longitudinal Survey. The two-level regression mixture analyses show that unobserved heterogeneity should not be presupposed to exist only at level 2 at the expense of level 1. Both the simulated and the real data analyses show that level 1 heterogeneity in the form of latent classes can be mistaken for level 2 heterogeneity in the form of the random effects that are used in conventional two-level regression analysis. Because of this, mixture models have an important role to play in multilevel regression analyses. Mixture models allow heterogeneity to be investigated more fully, more correctly attributing different portions of the heterogeneity to the different levels.     

从《中国大学评价》看长江大学的发展现状

现行的大学评价指标体系和排名方式,需要不断改进和完善;但这种以定量为主的评价方法,与传统的单纯定性评价的方式相比,具有直观清晰、数据客观的特点,说服力更强。分析《中国大学评价》对长江大学的排名,可为长江大学开展战略管理和年度发展评价提供一种新的视角。     

基于四叉树结构的小波格型矢量量化

基于格型矢量量化克服了传统矢量量化计算和存储复杂度高的缺点,提出了一种新型四叉树结构的小波格型矢量量化算法。对小波变换系数进行视觉加权,以感知的均方误差准则取代传统均方误差。改进零树编码方法,并按照小波系数的四叉树结构和其方向性来组织矢量,对重要系数作格型矢量量化。从而较好地综合利用了小波系数在空间和频域的能量集中特性。仿真实验证明,该方法具有速度快,存储量小的优点,与文献中其他算法相比,具有较高的编码效率。     

基于可变精度的加权粗糙集模型在约简中的研究

首先对粗糙集的定义进行了描述,在可变精度的基础上提出了加权粗糙集模型。重新定义了近似空间内的一些概念,给出了加权粗糙集模型的约简概念,指出了加权系数的两种方法。并根据实验分析,得出加权粗糙集模型约简中分类错误增大,约简长度越短,约简所花时间越长等特性。     

节能指标分解模型探析——基于甘肃省的实证分析

国家“十一五”规划提出,到2010年万元产值能耗降低20％。这个宏伟目标的实现对于我国经济增长和降低能源消耗具有重要意义。基于单位GDP能耗影响因素的分析,采用组合赋权的理论,对各影响因素进行合理的赋权,并在权重系数的基础上建构了节能目标由省到地级市分解的理论模型。然后根据构建的模型,利用甘肃省的经济和能耗数据对该省节能20％的目标向各地区科学、合理分解进行了探析。     

Experimental Games on Networks: Underpinnings of Behavior and Equilibrium Selection

In this paper, we describe a series of laboratory experiments that implement specific examples of a general network structure. Specifically, actions are either strategic substitutes or strategic complements, and participants have either complete or incomplete information about the structure of a random network. Since economic environments typically have a considerable degree of complementarity or substitutability, this framework applies to a wide variety of settings. We examine behavior and equilibrium selection. The degree of equilibrium play is striking, in particular with incomplete information. Behavior closely resembles the theoretical equilibrium whenever this is unique; when there are multiple equilibria, general features of networks, such as connectivity, clustering, and the degree of the players, help to predict informed behavior in the lab. People appear to be strongly attracted to maximizing aggregate payoffs (social efficiency), but there are forces that moderate this attraction: (1) people seem content with (in the aggregate) capturing only the lion's share of the efficient profits in exchange for reduced exposure to loss, and (2) uncertainty about the network structure makes it considerably more difficult to coordinate on a demanding, but efficient, equilibrium that is typically implemented with complete information.