Confidence intervals based on the deviance statistic for the hyperparameters in state space models

The main objective of this work is to evaluate the performance of confidence intervals, built using the deviance statistic, for the hyperparameters of state space models. The first procedure is a marginal approximation to confidence regions, based on the likelihood test, and the second one is based on the signed root deviance profile. Those methods are computationally efficient and are not affected by problems such as intervals with limits outside the parameter space, which can be the case when the focus is on the variances of the errors. The procedures are compared to the usual approaches existing in the literature, which includes the method based on the asymptotic distribution of the maximum likelihood estimator, as well as bootstrap confidence intervals. The comparison is performed via a Monte Carlo study, in order to establish empirically the advantages and disadvantages of each method. The results show that the methods based on the deviance statistic possess a better coverage rate than the asymptotic and bootstrap procedures.     

A comparative study of confidence intervals to assess biosimilarity from analytical data

Assessment of analytical similarity of tier 1 quality attributes is based on a set of hypotheses that tests the mean difference of reference and test products against a margin adjusted for standard deviation of the reference product. Thus, proper assessment of the biosimilarity hypothesis requires statistical tests that account for the uncertainty associated with the estimations of the mean differences and the standard deviation of the reference product. Recently, a linear reformulation of the biosimilarity hypothesis has been proposed, which facilitates development and implementation of statistical tests. These statistical tests account for the uncertainty in the estimation process of all the unknown parameters. In this paper, we survey methods for constructing confidence intervals for testing the linearized reformulation of the biosimilarity hypothesis and also compare the performance of the methods. We discuss test procedures using confidence intervals to make possible comparison among recently developed methods as well as other previously developed methods that have not been applied for demonstrating analytical similarity. A computer simulation study was conducted to compare the performance of the methods based on the ability to maintain the test size and power, as well as computational complexity. We demonstrate the methods using two example applications. At the end, we make recommendations concerning the use of the methods.     

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.     

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.     

Prediction of future failures times based on Type-I hybrid censored samples of random sample sizes

In this article, we consider the prediction of future failure times based on Type-I hybrid censored samples. Point predictors and prediction intervals using different procedures are discussed for a general model. The exponential and Rayleigh distributions are used as illustrative examples to show the most simplified forms of the so obtained predictors as well as prediction intervals. Intensive simulation study and a real life dataset are presented to illustrate our findings and results.     

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.     

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。