A New Proof of Murthy's Estimator which Applies to Sequential Sampling

Murthy's estimator has been used for constructing an unbiased estimator of a population total or mean from a sample of fixed size when there is unequal probability sampling without replacement. Traditionally, the estimator is derived by constructing an unordered version of Raj's ordered unbiased estimator. This paper presents an elementary proof of Murthy's estimator which applies the Rao–Blackwell theorem to a very simple estimator. This proof includes any sequential sampling scheme, thus extending the usefulness of Murthy's estimator. We demonstrate this extension by deriving unbiased estimators for inverse sampling.     

关于命运问题的理论思考

探讨命运问题的理论发展渊源,给出一个科学的唯物的命运观,不仅具有理论意义,更有重 大的实践意义。     

结构可靠性分析中蒙特卡洛模拟的应用

本文讨论了蒙特卡洛模拟在结构可靠性分析中的应用 ,并给出了直接抽样法中失效概率的计算公式和置信区间     

保险精算中的一个破产模型的改进

将古典的破产模型中的保险费收到的次数看作是复合泊松过程 ,将每次的保险费看作是服从指数分布的随机变量 ,从而对古典的破产模型进行了推广 ,并给出了相应的破产概率的上限。     

Assessment of futility in clinical trials

The term 'futility' is used to refer to the inability of a clinical trial to achieve its objectives. In particular, stopping a clinical trial when the interim results suggest that it is unlikely to achieve statistical significance can save resources that could be used on more promising research. There are various approaches that have been proposed to assess futility, including stochastic curtailment, predictive power, predictive probability, and group sequential methods. In this paper, we describe and contrast these approaches, and discuss several issues associated with futility analyses, such as ethical considerations, whether or not type I error can or should be reclaimed, one-sided vs two-sided futility rules, and the impact of futility analyses on power.     

Marginal regression models with a time to event outcome and discrete multiple source predictors

Information from multiple informants is frequently used to assess psychopathology. We consider marginal regression models with multiple informants as discrete predictors and a time to event outcome. We fit these models to data from the Stirling County Study; specifically, the models predict mortality from self report of psychiatric disorders and also predict mortality from physician report of psychiatric disorders. Previously, Horton et al. found little relationship between self and physician reports of psychopathology, but that the relationship of self report of psychopathology with mortality was similar to that of physician report of psychopathology with mortality. Generalized estimating equations (GEE) have been used to fit marginal models with multiple informant covariates; here we develop a maximum likelihood (ML) approach and show how it relates to the GEE approach. In a simple setting using a saturated model, the ML approach can be constructed to provide estimates that match those found using GEE. We extend the ML technique to consider multiple informant predictors with missingness and compare the method to using inverse probability weighted (IPW) GEE. Our simulation study illustrates that IPW GEE loses little efficiency compared with ML in the presence of monotone missingness. Our example data has non-monotone missingness; in this case, ML offers a modest decrease in variance compared with IPW GEE, particularly for estimating covariates in the marginal models. In more general settings, e.g., categorical predictors and piecewise exponential models, the likelihood parameters from the ML technique do not have the same interpretation as the GEE. Thus, the GEE is recommended to fit marginal models for its flexibility, ease of interpretation and comparable efficiency to ML in the presence of missing data.     

A frequentist understanding of sets of measures

We present a mathematical theory of objective, frequentist chance phenomena that uses as a model a set of probability measures. In this work, sets of measures are not viewed as a statistical compound hypothesis or as a tool for modeling imprecise subjective behavior. Instead we use sets of measures to model stable (although not stationary in the traditional stochastic sense) physical sources of finite time series data that have highly irregular behavior. Such models give a coarse-grained picture of the phenomena, keeping track of the range of the possible probabilities of the events. We present methods to simulate finite data sequences coming from a source modeled by a set of probability measures, and to estimate the model from finite time series data. The estimation of the set of probability measures is based on the analysis of a set of relative frequencies of events taken along subsequences selected by a collection of rules. In particular, we provide a universal methodology for finding a family of subsequence selection rules that can estimate any set of probability measures with high probability.     

Estimation of survival quantiles in two-stage randomization designs

In two-stage randomization designs, patients are randomized to one or more available therapies upon entry into the study. Depending on the response to the initial treatment (such as complete remission or shrinkage of tumor), patients are then randomized to receive maintenance treatments to maintain the response or salvage treatment to induce response. One goal of such trials is to compare the combinations of initial and maintenance or salvage therapies in the form of treatment strategies. In cases where the endpoint is defined as overall survival, Lunceford et al. [2002. Estimation of survival distributions of treatment policies in two-stage and randomization designs in clinical trials. Biometrics 58, 48–57] used mean survival time and pointwise survival probability to compare treatment strategies. But, mean survival time or survival probability at a specific time may not be a good summary representative of the overall distribution when the data are skewed or contain influential tail observations. In this article, we propose consistent and asymptotic normal estimators for percentiles of survival curves under various treatment strategies and demonstrate the use of percentiles for comparing treatment strategies. Small sample properties of these estimators are investigated using simulation. We demonstrate our methods by applying them to a leukemia clinical trial data set that motivated this research.     

Confidence limits and prediction limits for a Weibull distribution based on the generalized variable approach

In this article, we consider the problems of constructing confidence interval for a Weibull mean and setting prediction limits for future samples. Specifically, we construct upper prediction limits that include at least l$l$ of m$m$ samples from a Weibull distribution at each of r$r$ locations. The methods are based on the concept of generalized variable approach. The procedures can be easily extended to the type II censored samples, and they can be used to find approximate inferential procedures for type I censored samples. The proposed methods are conceptually simple and easy to use. The results are illustrated using some practical examples.     

青年婚配类型与夫妻关系——全国五大城市1216名已婚青年的调查分析

基于全国五大城市1216名已婚青年的调查资料,对目前城市青年家庭的不同婚配类型与夫妻关系之间的关联性进行探讨。研究结果表明,不同年龄匹配类型、不同文化程度匹配类型,以及不同收入水平匹配类型三个方面与青年家庭的夫妻关系状况无关;而不同城乡背景匹配类型、不同独生子女身份匹配类型两方面则与青年家庭的夫妻关系状况有关。研究揭示出,改革开放背景中成长的一代青年在个体特征上更具同质性,对他们的夫妻关系真正产生影响的因素,主要是他们在社会特征上的差别。今后的夫妻关系研究,在测量指标方面增加心理量表的内容或许是一个新的方向。