Asymptotic distributions for the intervals estimators of the extremal index and the cluster-size probabilities

Under appropriate long range dependence conditions, the point process of exceedances of a stationary sequence weakly converges to a homogeneous compound Poisson point process. This limiting point process can be characterized by the extremal index and the cluster-size probabilities. In this paper we address the problem of estimating these quantities and we consider the intervals estimators introduced in Ferro and Segers [2003. Inference for clusters of extreme values. J. Roy. Statist. Soc. Ser. B 545–556] and in Ferro [2004. Statistical methods for clusters of extreme values. Ph.D. Thesis, Lancaster University]. We establish asymptotic weak convergence to Gaussian random variables and we give their asymptotic variance.     

A note on new confidence intervals for the difference between two proportions based on an Edgeworth expansion

Zhou and Qin [2004. New intervals for the difference between two independent binomial proportions. J. Statist. Plann. Inference 123, 97–115; 2005. A new confidence interval for the difference between two binomial proportions of paired data. J. Statist. Plann. Inference 128, 527–542] “new confidence intervals” for the difference between two treatment proportions exhibit a severe lack of invariance property that is a compelling reason not to use them.     

Exact sample size determination in a weibull test plan when there is time censoring

Engineers who conduct reliability tests need to choose the sample size when designing a test plan. The model parameters and quantiles are the typical quantities of interest. The large-sample procedure relies on the property that the distribution of the t -like quantities is close to the standard normal in large samples. In this paper, we use a new procedure based on both simulation and asymptotic theory to determine the sample size for a test plan. Unlike the complete data case, the t -like quantities are not pivotal quantities in general when data are time censored. However we show that the distribution of the t -like quantities only depend on the expected proportion failing and obtain the distributions by simulation for both complete and time censoring case when data follow Weibull distribution. We find that the large-sample procedure usually underestimates the sample size even when it is said to be 200 or more. The sample size given by the proposed procedure insures the requested nominal accuracy and confidence of the estimation when the test plan results in complete or time censored data. Some useful figures displaying the required sample size for the new procedure are also presented.     

城市在职青年的生育时间选择及影响因素基于983名青年的实证调查分析

持续的低生育水平与少子化已经成为我国人口发展的新常态。生育时间的期望与选择作为生育意愿与行为的重要内涵之一,对生育水平具有重要影响。文章利用2020年10～12月在河北保定针对5大类行业18～35岁的983名在职青年所进行的“青年发展状况”问卷调查数据,对青年的个体社会特征与生育时间选择进行交互分析,在此基础上对影响在职青年最佳生育年龄选择的因素进行回归分析。结果显示：城市在职青年具有较强的晚育意识,其生育时间期望呈现出“男高女低”的特征,理想与打算二孩的生育间隔选择也相对趋近,从事教育行业、出生于城市、年龄较大、文化程度较高和“双独夫妇”的在职青年更倾向于选择晚生。多元线性回归分析结果表明,行业、年龄、文化程度、夫妇类型、性别和工作收入满意度均会显著影响青年的最佳生育年龄选择,其中教育行业、24～29岁年龄组、大专文化水平、“双独夫妇”对在职青年的最佳生育年龄期望具有明显的正向提升效应,女性比男性青年的最佳生育年龄期望更高,在职青年的工作收入满意度越高,则其最佳生育年龄偏好越晚。此外,文章也就晚婚晚育或不婚不育行为产生的影响、影响青年生育时间期望与选择的多重因素以及生育年龄期望与生育行为实践之间的差距展开了深入讨论,以进一步推进对育龄群体生育时间选择规律的认识和理解。     

Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm

Two new implementations of the EM algorithm are proposed for maximum likelihood fitting of generalized linear mixed models. Both methods use random (independent and identically distributed) sampling to construct Monte Carlo approximations at the E-step. One approach involves generating random samples from the exact conditional distribution of the random effects (given the data) by rejection sampling, using the marginal distribution as a candidate. The second method uses a multivariate t importance sampling approximation. In many applications the two methods are complementary. Rejection sampling is more efficient when sample sizes are small, whereas importance sampling is better with larger sample sizes. Monte Carlo approximation using random samples allows the Monte Carlo error at each iteration to be assessed by using standard central limit theory combined with Taylor series methods. Specifically, we construct a sandwich variance estimate for the maximizer at each approximate E-step. This suggests a rule for automatically increasing the Monte Carlo sample size after iterations in which the true EM step is swamped by Monte Carlo error. In contrast, techniques for assessing Monte Carlo error have not been developed for use with alternative implementations of Monte Carlo EM algorithms utilizing Markov chain Monte Carlo E-step approximations. Three different data sets, including the infamous salamander data of McCullagh and Nelder, are used to illustrate the techniques and to compare them with the alternatives. The results show that the methods proposed can be considerably more efficient than those based on Markov chain Monte Carlo algorithms. However, the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension.