The Singularity of the Information Matrix of the Mixed Proportional Hazard Model

This paper presents new identification conditions for the mixed proportional hazard model. In particular, the baseline hazard is assumed to be bounded away from 0 and ∞ near t = 0. These conditions ensure that the information matrix is nonsingular. The paper also presents an estimator for the mixed proportional hazard model that converges at rate N^−1/2.     

ESTIMATING A RATIO OF MEANS FROM BIVARIATE COUNTS WITH APPLICATIONS IN STEREOLOGY

In survey sampling and in stereology, it is often desirable to estimate the ratio of means θ= E(Y)/E(X) from bivariate count data (X, Y) with unknown joint distribution. We review methods that are available for this problem, with particular reference to stereological applications. We also develop new methods based on explicit statistical models for the data, and associated model diagnostics. The methods are tested on a stereological dataset. For point‐count data, binomial regression and bivariate binomial models are generally adequate. Intercept‐count data are often overdispersed relative to Poisson regression models, but adequately fitted by negative binomial regression.     

Multistate Survival Models as Transient Electrical Networks

In multistate survival analysis, the sojourn of a patient through various clinical states is shown to correspond to the diffusion of 1 C of electrical charge through an electrical network. The essential comparison has differentials of probability for the patient to correspond to differentials of charge, and it equates clinical states to electrical nodes. Indeed, if the death state of the patient corresponds to the sink node of the circuit, then the transient current that would be seen on an oscilloscope as the sink output is a plot of the probability density for the survival time of the patient. This electrical circuit analogy is further explored by considering the simplest possible survival model with two clinical states, alive and dead (sink), that incorporates censoring and truncation. The sink output seen on an oscilloscope is a plot of the Kaplan–Meier mass function. Thus, the Kaplan–Meier estimator finds motivation from the dynamics of current flow, as a fundamental physical law, rather than as a nonparametric maximum likelihood estimate (MLE). Generalization to competing risks settings with multiple death states (sinks) leads to cause‐specific Kaplan–Meier submass functions as outputs at sink nodes. With covariates present, the electrical analogy provides for an intuitive understanding of partial likelihood and various baseline hazard estimates often used with the proportional hazards model.     

Double bootstrap estimation of variance under systematic sampling with probability proportional to size

Variance estimation under systematic sampling with probability proportional to size is known to be a difficult problem. We attempt to tackle this problem by the bootstrap resampling method. It is shown that the usual way to bootstrap fails to give satisfactory variance estimates. As a remedy, we propose a double bootstrap method which is based on certain working models and involves two levels of resampling. Unlike existing methods which deal exclusively with the Horvitz–Thompson estimator, the double bootstrap method can be used to estimate the variance of any statistic. We illustrate this within the context of both mean and median estimation. Empirical results based on five natural populations are encouraging.     

Ordering results on extremes of scaled random variables with dependence and proportional hazards

This study deals with random variables equipped with Archimedean copulas and following scale proportional hazards (SPHs) or revered hazards models. We build the usual stochastic order both between minimums of two SPHs samples with Archimedean survival copulas and between maximums from two scale proportional reversed hazards (PRHs) samples with Archimedean copulas. The hazard rate order between minimums of independent SPHs samples and the reversed hazard rate order between maximums of independent scale PRHs samples are both derived. Also we have a discussion on the dispersive order between minimums from samples with a common Archimedean survival copula. The present results either generalize or improve some related ones in the recent literature.     

论县域内义务教育师资水平的均衡提升

教师资源不均衡是制约县域内义务教育均衡发展的瓶颈。义务教育均衡发展的制度设计及其实践探索,形成了可资完善发展的县域内义务教育学校师资水平均衡提升的方向及空间。县域内义务教育学校师资水平的均衡提升,客观上要求完善三级师范教育体系,注重师资的内培与外引,不断推进县域内"人走关系走"的教师全员周期性流动制度。     

Long-term effects of childbearing on mortality: Evidence from pre-industrial Sweden

This paper presents an analysis of the impact of childbearing history on later-life mortality for ever-married men and women using historical micro-level data of high quality for southern Sweden. The analysis uses a Cox proportional hazards model, estimating the effects on old-age mortality of number of births and timing of first and last births. By studying the effects of previous childbearing on mortality by sex and social status, we also gain important insights into the mechanisms relating childbearing to mortality in old age. The results show that number of children ever born had a statistically significant negative impact on longevity after age 50 for females but not for males. Analysis by social group shows that only landless women experienced higher mortality from having more children, which seems to indicate that the main explanations are to be found in social or economic conditions specific to females, rather than in the strictly biological or physiological effects of childbearing.     

Punitive Damages in China: Evolution and Application

Abstract

The revised Law on the Protection of the Rights and Interests of Consumers (Consumer Protection Law), which sums up nearly twenty years of the evolution of Chinese punitive damages regulations, sets out a model system of punitive damages. These are in essence a special kind of penalty under a dual public-private legal system in which the punitive and deterrent functions of public law are realized through the mechanism of private law. Their application should be guided by the public law principle that the penalty should be proportionate to the offence. The question of whether the penalty is appropriate arises in the application of the two forms of punitive damages prescribed in the Consumer Protection Law—whether used separately or together, or in conjunction with or independently of fines or financial awards. The application of the new punitive damages regulations may overlap with the application of China’s Food Safety Law and Tort Liability Law.     

失业保险给付期限差异下的失业持续时间研究

本文对享受不同失业保险给付期限的失业者的失业持续时间差异进行了实证研究。根据工作搜寻理论,应用存活分析方法建立了含有失业保险给付期限因素的失业持续时间模型,并对青岛市失业者登记数据进行了实证研究。结果表明:享受失业保险者的失业持续时间明显长于不享受失业保险者的失业持续时间,在失业保险给付额度相同的条件下,失业保险给付期限与失业持续时间成同向变动关系。     

Precedence tests and Lehmann alternatives

G = F ^k (k > 1); G = 1 − (1−F) ^k (k < 1); G = F ^k (k < 1); and G = 1 − (1−F) ^k (k > 1), where F and G are two continuous cumulative distribution functions. If an optimal precedence test (one with the maximal power) is determined for one of these four classes, the optimal tests for the other classes of alternatives can be derived. Application of this is given using the results of Lin and Sukhatme (1992) who derived the best precedence test for testing the null hypothesis that the lifetimes of two types of items on test have the same distibution. The test has maximum power for fixed κ in the class of alternatives G = 1 − (1−F) ^k , with k < 1. Best precedence tests for the other three classes of Lehmann-type alternatives are derived using their results. Finally, a comparison of precedence tests with Wilcoxon's two-sample test is presented. Received: February 22, 1999; revised version: June 7, 2000