Bayesian Interval Estimation for Predictive Values from Case-Control Studies

Positive predictive and negative predictive values (PPV and NPV) are often used to assess the accuracy of binary diagnostic tests. Unlike sensitivity and specificity, PPV and NPV are functions of the accuracy of the test and the overall prevalence of the disease in the population. In many studies of performance of estimators of PPV and NPV the population prevalence is assumed known. We allow for uncertainty in the estimate of the population prevalence and via simulation explore the impact of deviations from the assumed value.     

Exact Interval Estimation for the Scale Family Under General Progressive Type-II Censoring

In this article, we consider a general progressively Type-II censored life test where the lifetime distribution of each test unit belongs to the scale family. We derive an exact confidence interval for the scale parameter. Using Monte Carlo simulation method, we assess the expected lower and upper limits of the proposed confidence interval for the exponential distribution. Finally, we present a numerical example to illustrate the proposed procedure.     

Interval Estimation of the Stress-Strength Reliability with Independent Normal Random Variables

This article develops a procedure to obtain highly accurate confidence interval estimates for the stress-strength reliability R = P(X > Y) where X and Y are data from independent normal distributions of unknown means and variances. Our method is based on third-order likelihood analysis and is compared to the conventional first-order likelihood ratio procedure as well as the approximate methods of Reiser and Guttman (1986 Reiser, B., Guttman, I. (1986). Statistical inference for Pr(Y < X): the normal case. Technometrics 28: 253257.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Guo and Krishnamoorthy (2004 Guo, H., Krishnamoorthy, K. (2004). New approximate inferential methods for the reliability parameter in a stress-strength model: the normal case. Commun. Statist. Theor. Meth. 33: 17151731.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The use of our proposed method is illustrated by an empirical example and its superior accuracy in terms of coverage probability and error rate are examined through Monte Carlo simulation studies.     

On a Confidence Interval for the Mean of an Asymmetric Distribution

A clarification is given of the main result (1.1) in Communications in Statistics: Theory and Methods 34:753–766. The term {1 + 6a(r ? a)}^1/3 is to be understood as sgn(1 + 6a(r ? a)) | 1 + 6a(r ? a)|^1/3. The result is expressed in a more user-friendly form. An issue is raised regarding the common usage of the expression x ^1/n when n is even.     

基尼系数的区间估计及其应用

 本文给出了收入为离散分布的三种计算基尼系数的新方法。利用收入份额法导出了基尼系数协方差算法的离散形式,并因此产生了计算基尼系数的回归系数法。文章重点讨论了基尼系数进行区间估计的两种方法,这些方法也适用于集中度指数,因而它们在测度社会经济领域的不平等中具有着十分广泛的用途。实际应用表明,新算法有效地简化了对基尼系数区间估计的标准差估算。     

中国农民工汇款的影响因素分析——一个区间回归模型的应用

 摘　　要:中国农村劳动力的大规模转移，为劳动力输出地带来了大量汇款，这些汇款甚至超过了当地的财政收入。在本文中，我们利用最近所做的农民工汇款问卷调查数据来分析影响农民工汇款的因素。因为关于汇款量的调查数据处于不同的区间而不是具体的数值，所以我们利用区间回归模型来对此进行分析。研究结果表明，农民工的打工收入、农村老家的非汇款收入、农村老家的耕地数量以及农民工的年龄对汇款量具有显著的正向影响，而农民工的转移成本、是否全家一起外出打工、是否有失业经历以及是否接受过大学教育对汇款量具有显著的负向影响 。     

Likelihood Ratio Tests for Interval Hypotheses with Applications

In this article, we derive the likelihood ratio tests (LRTs) for simultaneously testing interval hypotheses for normal means with known and unknown variances, and also with unknown but equal variance. Special cases when the interval hypotheses boil down to a point hypothesis are also discussed. Remarks regarding comparison of the LRT with tests based on combination of p-values are made, and several applications based on real data are mentioned.     

Interval estimation for exponential progressive Type-II censored step-stress accelerated life-testing

This paper derives the exact confidence intervals for the exponential step-stress accelerated life-testing model as well as the approximate confidence intervals for the k-step exponential step-stress accelerated life-testing model under progressive Type-II censoring. A Monte Carlo simulation study is carried out to examine the performance of these confidence intervals. Finally, an example is given to illustrate the proposed procedures.     

Nonparametric versus Parametric Estimation of the Cure Fraction Using Interval Censored Data

This article discusses estimation of the cure rate by means of the bounded cumulative hazard (BCH) model using interval censored data. The parametric and nonparametric estimation methods within the framework of the EM algorithm were employed for cure rate estimation and their results compared. The Turnbull estimator was used in the nonparametric estimation while in parametric method both the exponential and Weibull distributions were considered. We show via simulation that the nonparametric method is a viable alternative to the parametric one when the censoring rate is rapidly increasing.     

Interval estimation for a lower-truncated distribution based on the double Type-II censored sample

ABSTRACT

The interval estimation problem is investigated for the parameters of a general lower truncated distribution under double Type-II censoring scheme. The exact, asymptotic and bootstrap interval estimates are derived for the unknown model parameter and the lower truncated threshold bound. One real-life example and a numerical study are presented to illustrate performance of our methods.     

Point and Interval Estimations of Marginal Risk Difference by Logistic Model

We use logistic model to get point and interval estimates of the marginal risk difference in observational studies and randomized trials with dichotomous outcome. We prove that the maximum likelihood estimate of the marginal risk difference is unbiased for finite sample and highly robust to the effects of dispersing covariates. We use approximate normal distribution of the maximum likelihood estimates of the logistic model parameters to get approximate distribution of the maximum likelihood estimate of the marginal risk difference and then the interval estimate of the marginal risk difference. We illustrate application of the method by a real medical example.     

Statistical Analysis of Exponential Lifetimes Under an Integrated Type-Ii Interval Censoring Scheme

In this paper, we propose a new type of censoring scheme which combines the features of grouped censoring and Type-II censoring. Statistical analysis of exponentially distributed lifetimes observed under this scheme is considered. The MLE of the model parameter and its asymptotic variance are derived. Furthermore, expressions for the expected experiment time and the expected number of failures are given. A numerical study is conducted to study these quantities and the results are compared with those under a Type-II censored plan. This comparison provides useful insight on the choice of these plans in designing a life test.     

A Comparison of Approaches to Interval Estimation of Mediated Effects in Linear Regression Models

A novel approach based on the concepts of a generalized pivotal quantity (GPQ) is developed to construct confidence intervals for the mediated effect. Thereafter, its performance is compared with six interval estimation approaches in terms of empirical coverage probability and expected length via simulation and two real examples. The results show that the GPQ-based and bootstrap percentile methods outperform other methods when mediated effects exist in small and medium samples. Moreover, the GPQ-based method exhibits a more stable performance in small and non-normal samples. A discussion on how to choose the best interval estimation method for mediated effects is presented.     

A Bayesian Approach for Selecting the Best Exponential Population with Interval Censored Samples

In this article, we study the problem of selecting the best population from among several exponential populations based on interval censored samples using a Bayesian approach. A Bayes selection procedure and a curtailed Bayes selection procedure are derived. We show that these two Bayes selection procedures are equivalent. A numerical example is provided to illustrate the application of the two selection procedure. We also use Monte Carlo simulation to study performance of the two selection procedures. The numerical results of the simulation study demonstrate that the curtailed Bayes selection procedure has good performance because it can substantially reduce the duration time of life test experiment.     

Modifications of the Empirical Likelihood Interval Estimation with Improved Coverage Probabilities

The empirical likelihood (EL) technique has been well addressed in both the theoretical and applied literature in the context of powerful nonparametric statistical methods for testing and interval estimations. A nonparametric version of Wilks theorem (Wilks, 1938 Wilks , S. S. ( 1938 ). The large-sample distribution of the likelihood ratio for testing composite hypotheses . Annals of Mathematical Statistics 9 : 60 – 62 .[Crossref] , [Google Scholar]) can usually provide an asymptotic evaluation of the Type I error of EL ratio-type tests. In this article, we examine the performance of this asymptotic result when the EL is based on finite samples that are from various distributions. In the context of the Type I error control, we show that the classical EL procedure and the Student's t-test have asymptotically a similar structure. Thus, we conclude that modifications of t-type tests can be adopted to improve the EL ratio test. We propose the application of the Chen (1995 Chen , L. ( 1995 ). Testing the mean of skewed distributions . Journal of the American Statistical Association 90 : 767 – 772 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) t-test modification to the EL ratio test. We display that the Chen approach leads to a location change of observed data whereas the classical Bartlett method is known to be a scale correction of the data distribution. Finally, we modify the EL ratio test via both the Chen and Bartlett corrections. We support our argument with theoretical proofs as well as a Monte Carlo study. A real data example studies the proposed approach in practice.     

人均GDP翻两番: 年均增长率的区间估算

 “实现人均GDP到二０二０年比二０００年翻两番”是十七大报告中的一个崭新提法,它为我们清晰地描绘了中国在重要战略机遇期应当达到的基本发展目标。本文在考虑人口自然增长率时间序列数据变化的基础上,采用移动平均数法和增长率的数学分解法,对达到上述发展目标的人均GDP年平均增长率与实际GDP年平均增长率进行了区间估算,估算的结果表明：必须继续严格执行计划生育政策、控制好各个时期的经济增长速度、保证宏观调控政策落到实处并完成十七大提出的各项配套任务,才能使人均GDP翻两番的发展目标在科学发展观的框架下得到充分实现。     

Dependence Models Arising from the Lagrangian Probability Distributions

In this article, we propose a method based on the Lagrangian probability distributions for developing new dependence models. Specifically, a generalized Poisson–gamma dependence model is derived. The maximum likelihood estimation (MLE) technique is proposed for estimating the dependence model parameters. Application of the generalized Poisson–gamma dependence model is illustrated by using an operational risks dataset.     

流动人口女性个体的生育间隔影响因素研究——基于2016年全国流动人口动态监测调查数据

本文采用2016年全国流动人口动态监测调查数据,运用半参数Cox回归对我国流动人口的生育间隔进行分析。结果发现：第一,不仅人口流动会延迟女性的生育时间,而且受教育水平的提高对女性的婚育间隔、第一次生育间隔均有显著的延迟效应。第二,结婚年龄越大,婚后越有可能选择尽早生育,且不同初婚时间对生育间隔的影响差异明显。同时,参加医疗保险对婚育间隔存在显著的缩短效应,而参加生育保险对生育间隔存在显著的延迟效应。越有经济实力以及在工作中担任重要职位的女性越有可能扩大生育间隔;而随着婚育间隔的扩大,第一次生育间隔反而会缩短。第三,初育子女的性别对第一次生育间隔的影响存在显著差异,即若初次生育为女性,则第一次生育间隔会缩短。第四,根据生育政策效果分析发现,放开生育政策虽无法促使女性缩短婚育间隔,但会明显缩短第一次生育间隔。     

More Powerful Tests from Confidence Interval p Values

In this article the problem of comparing two independent binomial populations is considered. It is shown that the test based on the confidence interval p value of Berger and Boos often is uniformly more powerful than the standard unconditional test. This test also requires less computational time.