Statistical inference for start-up demonstration tests with rejection of units upon observing d failures

In this paper, we consider the statistical inference for the success probability in the case of start-up demonstration tests in which rejection of units is possible when a pre-fixed number of failures is observed before the required number of consecutive successes are achieved for acceptance of the unit. Since the expected value of the stopping time is not a monotone function of the unknown parameter, the method of moments is not useful in this situation. Therefore, we discuss two estimation methods for the success probability: (1) the maximum likelihood estimation (MLE) via the expectation-maximization (EM) algorithm and (2) Bayesian estimation with a beta prior. We examine the small-sample properties of the MLE and Bayesian estimator. Finally, we present an example to illustrate the method of inference discussed here.     

On some pre-test and Stein-rule phi-divergence test estimators in the independence model of categorical data

For the model of independence in a two way contingency table, shrinkage estimators based on minimum φ$\phi$-divergence estimators and φ$\phi$-divergence statistics are considered. These estimators are based on the James–Stein-type rule and incorporate the idea of preliminary test estimator. The asymptotic bias and risk are obtained under contiguous alternative hypotheses, and on the basis of them a comparison study is carried out.     

双重分层抽样中的校正估计

校正估计法已被大量运用于抽样调查中,它利用辅助信息构造的校正权重提高了对总体总值（或均值）的估计精度。本文提出了分层抽样中的校正组合比率估计量,并推广到分层双重抽样中。同时给出新估计量的近似方差表达式。最后利用计算机随机模拟验证较正估计量对估计精度的改进。     

Estimating the grid of time-points for the piecewise exponential model

One of the greatest challenges related to the use of piecewise exponential models (PEMs) is to find an adequate grid of time-points needed in its construction. In general, the number of intervals in such a grid and the position of their endpoints are ad-hoc choices. We extend previous works by introducing a full Bayesian approach for the piecewise exponential model in which the grid of time-points (and, consequently, the endpoints and the number of intervals) is random. We estimate the failure rates using the proposed procedure and compare the results with the non-parametric piecewise exponential estimates. Estimates for the survival function using the most probable partition are compared with the Kaplan-Meier estimators (KMEs). A sensitivity analysis for the proposed model is provided considering different prior specifications for the failure rates and for the grid. We also evaluate the effect of different percentage of censoring observations in the estimates. An application to a real data set is also provided. We notice that the posteriors are strongly influenced by prior specifications, mainly for the failure rates parameters. Thus, the priors must be fairly built, say, really disclosing the expert prior opinion.     

Nonparametric confidence intervals for Tmax in sequence-stratified crossover studies

Tmax is the time associated with the maximum serum or plasma drug concentration achieved following a dose. While Tmax is continuous in theory, it is usually discrete in practice because it is equated to a nominal sampling time in the noncompartmental pharmacokinetics approach. For a 2-treatment crossover design, a Hodges-Lehmann method exists for a confidence interval on treatment differences. For appropriately designed crossover studies with more than two treatments, a new median-scaling method is proposed to obtain estimates and confidence intervals for treatment effects. A simulation study was done comparing this new method with two previously described rank-based nonparametric methods, a stratified ranks method and a signed ranks method due to Ohrvik. The Normal theory, a nonparametric confidence interval approach without adjustment for periods, and a nonparametric bootstrap method were also compared. Results show that less dense sampling and period effects cause increases in confidence interval length. The Normal theory method can be liberal (i.e. less than nominal coverage) if there is a true treatment effect. The nonparametric methods tend to be conservative with regard to coverage probability and among them the median-scaling method is least conservative and has shortest confidence intervals. The stratified ranks method was the most conservative and had very long confidence intervals. The bootstrap method was generally less conservative than the median-scaling method, but it tended to have longer confidence intervals. Overall, the median-scaling method had the best combination of coverage and confidence interval length. All methods performed adequately with respect to bias.     

Estimation and Confidence Regions for Parameter Sets in Econometric Models1

This paper develops a framework for performing estimation and inference in econometric models with partial identification, focusing particularly on models characterized by moment inequalities and equalities. Applications of this framework include the analysis of game‐theoretic models, revealed preference restrictions, regressions with missing and corrupted data, auction models, structural quantile regressions, and asset pricing models. Specifically, we provide estimators and confidence regions for the set of minimizers Θ_I of an econometric criterion function Q(θ). In applications, the criterion function embodies testable restrictions on economic models. A parameter value θthat describes an economic model satisfies these restrictions if Q(θ) attains its minimum at this value. Interest therefore focuses on the set of minimizers, called the identified set. We use the inversion of the sample analog, Q_n(θ), of the population criterion, Q(θ), to construct estimators and confidence regions for the identified set, and develop consistency, rates of convergence, and inference results for these estimators and regions. To derive these results, we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification.     

Heuristic Coordination of Decentralized Inventory Systems Using Induced Backorder Costs

In this paper, we investigate a one‐warehouse multiple‐retailer system, where the inventory control decisions are coordinated using a near optimal induced backorder cost, β*. All installations use continuous review installation‐stock (R, Q) policies. The analysis builds on an approximation model where the stochastic warehouse delays are replaced by their correct averages. The contributions include insights as to how β* is influenced by system parameters, and the determination of simple closed form β* estimates. The latter offering a practical means to achieve coordinated control of large size systems.     

Generalized inferences on the common mean vector of several multivariate normal populations

The hypothesis testing and confidence region are considered for the common mean vector of several multivariate normal populations when the covariance matrices are unknown and possibly unequal. A generalized confidence region is derived using the concepts of generalized method based on the generalized p$p$-value. The generalized confidence region is illustrated with two numerical examples. The merits of the proposed method are numerically compared with those of existing methods with respect to their expected area or expected d-dimensional volumes and coverage probabilities under different scenarios.     

供应链物流运作能力计划模型与分析

考察了某种产品供应链系统的一次性物流运作过程,建立了这个系统的物流能力动态规划模型。针对供应链中物流运作能力的流通量指标进行了较为深入的理论分析,探讨了使得系统成本最小化的最优物流能力及系统各阶段需配置的流通量。最优物流能力策略体现为两个关键量,即下界和上界。如果可得输入量小于下界则选择不开展物流;如果可得输入超出了下界,物流能力可以足够大但不超过上界。运用数学归纳法对优化结果进行了证明,并结合算例检验了模型的效果。