Performance of Confidence Intervals in Regression Models with Unbalanced One-Fold Nested Error Structures

Abstract

In this article we consider the problem of constructing confidence intervals for a linear regression model with unbalanced nested error structure. A popular approach is the likelihood-based method employed by PROC MIXED of SAS. In this article, we examine the ability of MIXED to produce confidence intervals that maintain the stated confidence coefficient. Our results suggest that intervals for the regression coefficients work well, but intervals for the variance component associated with the primary level cannot be recommended. Accordingly, we propose alternative methods for constructing confidence intervals on the primary level variance component. Computer simulation is used to compare the proposed methods. A numerical example and SAS code are provided to demonstrate the methods.     

基于贝叶斯的Bootstrap置信区间

在许多领域中,Bootstrap成为一种数据处理的有效方法。很多情况下,模型中感兴趣的参数的置信区间难以构建,为了解决这一问题,文章提出了一个新的贝叶斯Bootstrap置信区间的估计量,并做了蒙特卡洛模拟比较,结果比经典区间估计方法和经典Bootstrap方法更优,并进行了实例分析。     

小学新任教师职业自信问题及对策

刚步入小学教师岗位的新任教师,在角色转换中往往会产生诸多的不适应,难免陷入自卑的泥潭,丧失职业自信,甚至产生辞职想法。为此,要客观认识新任教师阶段,建立教育信念与信仰,全面看待学生成绩的“进退”,做好SWOT分析与教学笔记,利用网络资源和线下交流学习,提升职业自信与职业能力。     

大学生学科文化自信培育的价值逻辑及路径探析 ——以河北工程大学地球科学与工程学院为例

学科文化是学科的灵魂,是学科不断发展创新的精神源泉和内在动力。学科文化自信是文化自信的重要组成部分,培育大学生文化自信应着眼全局,整体推进。学科文化自信与文化自信具有统一性,与核心价值观培育具有同构性,与担当民族复兴大任具有生成性。培育大学生学科文化自信,要深入挖掘和整合学科文化内涵,不断创新和发展培育手段,最终达到浸润和形塑博学自信的新时代大学生的目标。学科文化自信的培育可以达到激发学生学术热情,促进学生和学科全面发展,弘扬社会主义核心价值观,坚定理想信念以及践行使命担当的效用。     

中国共产党开创中国式现代化道路的历史意义和世界贡献

中国共产党百年奋斗征程中将马克思主义与中国实际相结合,开创了中国式现代化道路。这是中华民族自主探索现代化道路的开始,也是民族自立自信的基石;中国式现代化道路是科学社会主义基本原则与中国具体实际相结合的产物,是对科学社会主义创新发展的成功样本;中国式现代化道路实现了从资本逻辑主导的西方现代化模式向以人民为中心的现代化模式的转变;促使世界历史进程从西方垄断现代化叙事向世界各民族自主选择现代化道路转变;中国式现代化道路集人类文明之精华,开创了人类文明的新形态,为世界发展和人类共同进步作出重要贡献。     

重塑学生自信心的情感教学法初探

现代教育培养的人才应具有健全的人格、较强的创新精神和实践能力,善于协作和敢于竞争.然而,目前高校中有相当一部分学生因为学习成绩差等原因而丧失自信心,陷入不良情感的心理障碍中不能自拔.基于人本主义学习理论的情感教学法注重教学过程中的师生互动和情感交流,能够有效地促使学生重塑自信心,恢复积极向上的健康心态.情感教学法可从五个环节来实施:(1)简介课程的概况,确立课程的学习目标,对学生进行积极的鼓励;(2)调查学生的情况,将学生进行合理分组;(3)在教学过程中将课程知识传授、能力培养与信心培养相结合;(4)实行阶段考察,鼓励学生进一步学习;(5)课程结束时对"差生"实施积极的补救措施.     

When is n large enough? Looking for the right sample size to estimate proportions

The central limit theorem indicates that when the sample size goes to infinite, the sampling distribution of means tends to follow a normal distribution; it is the basis for the most usual confidence interval and sample size formulas. This study analyzes what sample size is large enough to assume that the distribution of the estimator of a proportion follows a Normal distribution. Also, we propose the use of a correction factor in sample size formulas to ensure a confidence level even when the central limit theorem does not apply for these distributions.     

Stress-strength reliability of exponentiated Fréchet distributions based on Type-II censored data

In this paper, we consider inference of the stress-strength parameter, R, based on two independent Type-II censored samples from exponentiated Fréchet populations with different index parameters. The maximum likelihood and uniformly minimum variance unbiased estimators, exact and asymptotic confidence intervals and hypotheses testing for R are obtained. We conduct a Monte Carlo simulation study to evaluate the performance of these estimators and confidence intervals. Finally, two real data sets are analysed for illustrative purposes.     

Progressive censoring with fixed censoring times

In this paper, we revisit the progressive Type-I censoring scheme as it has originally been introduced by Cohen [Progressively censored samples in life testing. Technometrics. 1963;5(3):327–339]. In fact, original progressive Type-I censoring proceeds as progressive Type-II censoring but with fixed censoring times instead of failure time based censoring times. Apparently, a time truncation has been added to this censoring scheme by interpreting the final censoring time as a termination time. Therefore, not much work has been done on Cohens's original progressive censoring scheme with fixed censoring times. Thus, we discuss distributional results for this scheme and establish exact distributional results in likelihood inference for exponentially distributed lifetimes. In particular, we obtain the exact distribution of the maximum likelihood estimator (MLE). Further, the stochastic monotonicity of the MLE is verified in order to construct exact confidence intervals for both the scale parameter and the reliability.     

Theoretical results on the discrete Weibull distribution of Nakagawa and Osaki

In this paper, we discuss some theoretical results and properties of the discrete Weibull distribution, which was introduced by Nakagawa and Osaki [The discrete Weibull distribution. IEEE Trans Reliab. 1975;24:300–301]. We study the monotonicity of the probability mass, survival and hazard functions. Moreover, reliability, moments, p-quantiles, entropies and order statistics are also studied. We consider likelihood-based methods to estimate the model parameters based on complete and censored samples, and to derive confidence intervals. We also consider two additional methods to estimate the model parameters. The uniqueness of the maximum likelihood estimate of one of the parameters that index the discrete Weibull model is discussed. Numerical evaluation of the considered model is performed by Monte Carlo simulations. For illustrative purposes, two real data sets are analyzed.