Mean estimate in ranked set sampling using a length-biased concomitant variable

In this paper, a ranked set sampling procedure with ranking based on a length-biased concomitant variable is proposed. The estimate for population mean based on this sample is given. It is proved that the estimate based on ranked set samples is asymptotically more efficient than the estimate based on simple random samples. Simulation studies are conducted to present the properties of the proposed estimate for finite sample size. Moreover, the consequence of ignoring length bias is also addressed by simulation studies and the real data analysis.     

Computing the Cox Model for Case Cohort Designs

Prentice (1986) proposed a case-cohort design as an efficient subsampling mechanism for survival studies. Several other authors have expanded on these ideas to create a family of related sampling plans, along with estimators for the covariate effects. We describe how to obtain the proposed parameter estimates and their variance estimates using standard software packages, with SAS and SPLUS as particular examples.     

生长曲线最小二乘估计和最佳线性无偏估计相等的几个充要条件

讨论了生长曲线未知参数的最小二乘估计与最佳线性无偏估计相等的几个充要条件,并给出了主要结论的两种不同证明。     

On the robustness of empirical likelihood ratio confidence intervals for location

The authors examine the robustness of empirical likelihood ratio (ELR) confidence intervals for the mean and M‐estimate of location. They show that the ELR interval for the mean has an asymptotic breakdown point of zero. They also give a formula for computing the breakdown point of the ELR interval for M‐estimate. Through a numerical study, they further examine the relative advantages of the ELR interval to the commonly used confidence intervals based on the asymptotic distribution of the M‐estimate.     

Properties of Model-Averaged BMDLs: A Study of Model Averaging in Dichotomous Response Risk Estimation

Model averaging (MA) has been proposed as a method of accounting for model uncertainty in benchmark dose (BMD) estimation. The technique has been used to average BMD dose estimates derived from dichotomous dose-response experiments, microbial dose-response experiments, as well as observational epidemiological studies. While MA is a promising tool for the risk assessor, a previous study suggested that the simple strategy of averaging individual models' BMD lower limits did not yield interval estimators that met nominal coverage levels in certain situations, and this performance was very sensitive to the underlying model space chosen. We present a different, more computationally intensive, approach in which the BMD is estimated using the average dose-response model and the corresponding benchmark dose lower bound (BMDL) is computed by bootstrapping. This method is illustrated with TiO(2) dose-response rat lung cancer data, and then systematically studied through an extensive Monte Carlo simulation. The results of this study suggest that the MA-BMD, estimated using this technique, performs better, in terms of bias and coverage, than the previous MA methodology. Further, the MA-BMDL achieves nominal coverage in most cases, and is superior to picking the "best fitting model" when estimating the benchmark dose. Although these results show utility of MA for benchmark dose risk estimation, they continue to highlight the importance of choosing an adequate model space as well as proper model fit diagnostics.     

Survival analysis for the inverse Gaussian distribution with the Gibbs sampler

This paper describes a comprehensive survival analysis for the inverse Gaussian distribution employing Bayesian and Fiducial approaches. It focuses on making inferences on the inverse Gaussian (IG) parameters μ and λ and the average remaining time of censored units. A flexible Gibbs sampling approach applicable in the presence of censoring is discussed and illustrations with Type II, progressive Type II, and random rightly censored observations are included. The analyses are performed using both simulated IG data and empirical data examples. Further, the bootstrap comparisons are made between the Bayesian and Fiducial estimates. It is concluded that the shape parameter ( ϕ=λ/μ) of the inverse Gaussian distribution has the most impact on the two analyses, Bayesian vs. Fiducial, and so does the size of censoring in data to a lesser extent. Overall, both these approaches are effective in estimating IG parameters and the average remaining lifetime. The suggested Gibbs sampler allowed a great deal of flexibility in implementation for all types of censoring considered.     

广义Gamma分布簇广义线性混合模型的构建

 本文在广义Gamma分布簇基础上引入异质性来构建广义线性混合模型。本文构建的广义Gamma分布簇广义线性混合模型在广义线性混合模型的框架下分析,通过参数重整技术把广义Gamma分布簇变量的建模问题与指数分布簇变量的建模问题联系起来,模型推断可以方便地利用广义线性混合模型和广义线性模型的研究成果,同时也可以方便地推广到其他模型。三参数广义Gamma分布可以收缩到两参数的Gamma分布、Weibull分布或指数分布,能降低模型误设的风险,还能便利地分析误差结构。     

Estimation of system reliability

In this paper, we estimate the reliability of a system with k components. The system functions when at least s (1≤s≤k) components survive a common random stress. We assume that the strengths of these k components are subjected to a common stress which is independent of the strengths of these k components. If (X ₁,X ₂,…,X _k ) are strengths of k components subjected to a common stress (Y), then the reliability of the system or system reliability is given byR=P[Y<X _(k−s+1)] whereX _(k−s+1) is (k−s+1)-th order statistic of (X ₁,…,X _k ). We estimate R when (X ₁,…,X _k ) follow an absolutely continuous multivariate exponential (ACMVE) distribution of Hanagal (1993) which is the submodel of Block (1975) and Y follows an independent exponential distribution. We also obtain the asymptotic normal (AN) distribution of the proposed estimator.     

Le problème d'Anscombe pour les lois binomiales négatives généralisées

Consider a finite sample from a generalized negative-binomial distribution where both (canonical and index) parameters are unknown. This note proves that both the maximum-likelihood estimate and the moment estimate of the index parameter exist if and only if the sample variance is greater than the sample mean. This extends a result for the negative-binomial distribution that had been conjectured by Anscombe (1950) and later shown by Levin and Reeds (1977).     

Convergence properties of the EM algorithm in constrained parameter spaces

The established general results on convergence properties of the EM algorithm require the sequence of EM parameter estimates to fall in the interior of the parameter space over which the likelihood is being maximized. This paper presents convergence properties of the EM sequence of likelihood values and parameter estimates in constrained parameter spaces for which the sequence of EM parameter estimates may converge to the boundary of the constrained parameter space contained in the interior of the unconstrained parameter space. Examples of the behavior of the EM algorithm applied to such parameter spaces are presented.