Exact average coverage probabilities and confidence coefficients of confidence intervals for discrete distributions

For a confidence interval (L(X),U(X)) of a parameter θ in one-parameter discrete distributions, the coverage probability is a variable function of θ. The confidence coefficient is the infimum of the coverage probabilities, inf  _θ P _θ (θ∈(L(X),U(X))). Since we do not know which point in the parameter space the infimum coverage probability occurs at, the exact confidence coefficients are unknown. Beside confidence coefficients, evaluation of a confidence intervals can be based on the average coverage probability. Usually, the exact average probability is also unknown and it was approximated by taking the mean of the coverage probabilities at some randomly chosen points in the parameter space. In this article, methodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions are proposed. With these methodologies, both exact values can be derived.     

论青年女性流动人口初育间隔与人口控制——来自厦门流动人口家庭问卷调查的启示

青年女性流动人口实际生育行为的控制对于人口规模与结构的控制,起着至关重要的作用。而生育时间的选择作为影响流动人口生育实践的一个重要因素,体现在对各孩次生育间隔的控制上。本文在描述分析的基础上,应用Cox比例风险模型,主要对厦门市青年女性流动人口初育间隔的影响因素进行估计和检验,并在总结分析的基础上对流动人口控制问题提出几点对策思考。     

"中国信心":当代中华民族凝聚力的现实解读

"中国信心"不仅仅是一个新闻词汇或政治口号,而是引领当代中国社会发展的民族精神和时代精神的精华.在内涵上,"中国信心"是民族性与时代性的辩证统一,是中国特色社会主义理论体系的重要内容;在本质上,"中国信心"是成就感与使命感的高度结合,是社会主义精神文明建设的时代展示;在功能定位上,"中国信心"是当代中华民族凝聚力增强的鲜明亮点,对提升国家文化软实力具有重要意义.     

Can Likert Scales be Treated as Interval Scales?—A Simulation Study

The Likert scale is widely used in social work research, and is commonly constructed with four to seven points. It is usually treated as an interval scale, but strictly speaking it is an ordinal scale, where arithmetic operations cannot be conducted. There are pros and cons in using the Likert scale as an interval scale, but the controversy can be handled by increasing the number of points. Several researchers have suggested bringing the number up to eleven, on the basis of empirical data. In this article the authors explore this rational and share the same view, but simulate artificial data from both symmetrical normal and skewed distributions where the underlying metric is known in advance. Results show that more Likert scale points will result in a closer approach to the underlying distribution, and hence normality and interval scales. To increase generalizability social work practitioners are encouraged to use 11-point Likert scales from 0 to 10, a natural and easily comprehensible range.     

Is Gaydar Affected by Attitudes Toward Homosexuality? Confidence,Labeling Bias,and Accuracy

Previous research has largely ignored the relationship between sexual orientation judgement accuracy, confidence, and attitudes toward homosexuality. In an online study, participants (N = 269) judged the sexual orientation of homosexual and heterosexual targets presented via a series of facial photographs. Participants also indicated their confidence in each judgment and completed the Modern Homonegativity Scale (Morrison & Morrison, 2002). We found that (1) homosexual men and heterosexual women were more accurate when judging photographs of women as opposed to photographs of men, and (2) in heterosexual men, negative attitudes toward homosexual men predicted confidence and bias when rating men’s photographs. Findings indicate that homosexual men and heterosexual women are similar in terms of accuracy in judging women’s sexuality. Further, especially in men, homophobia is associated with cognitive biases in labeling other men but does not have a relationship with increased accuracy.     

Seeking Clarity and Confidence in the Divorce Decision-Making Process

There is a well-established literature dedicated to why couples divorce, transitions associated with divorce, and the impact of divorce on families. However, little is known about the divorce decision-making process. We conducted in-depth interviews with individuals who have recently considered divorce (n = 30) and asked specifically about the roles of 2 concepts in their decision-making process: clarity and confidence. Three major themes emerged from the data: (a) Clarity about a decision to divorce or stay married is desired, it fluctuates, and takes time to find; (b) pivotal moments can bring clarity; and (c) confidence (in the final decision) is desired. Clinical implications and directions for future research are discussed.     

Likelihood inference for the component lifetime distribution based on progressively censored parallel systems data

Point and interval estimators for the scale parameter of the component lifetime distribution of a k-component parallel system are obtained when the component lifetimes are assumed to be independently and identically exponentially distributed. We prove that the maximum likelihood estimator of the scale parameter based on progressively Type-II censored system lifetimes is unique and can be obtained by a fixed-point iteration procedure. In particular, we illustrate that the Newton–Raphson method does not converge for any initial value. Furthermore, exact confidence intervals are constructed by a transformation using normalized spacings and other component lifetime distributions including Weibull distribution are discussed.     

Approximate Bayesianity of Frequentist Confidence Intervals for a Binomial Proportion

The well-known Wilson and Agresti–Coull confidence intervals for a binomial proportion p are centered around a Bayesian estimator. Using this as a starting point, similarities between frequentist confidence intervals for proportions and Bayesian credible intervals based on low-informative priors are studied using asymptotic expansions. A Bayesian motivation for a large class of frequentist confidence intervals is provided. It is shown that the likelihood ratio interval for p approximates a Bayesian credible interval based on Kerman’s neutral noninformative conjugate prior up to O(n^{? 1}) in the confidence bounds. For the significance level α ? 0.317, the Bayesian interval based on the Jeffreys’ prior is then shown to be a compromise between the likelihood ratio and Wilson intervals. Supplementary materials for this article are available online.     

Generalized simultaneous confidence regions for regression coefficients and their ratios

This study constructs a simultaneous confidence region for two combinations of coefficients of linear models and their ratios based on the concept of generalized pivotal quantities. Many biological studies, such as those on genetics, assessment of drug effectiveness, and health economics, are interested in a comparison of several dose groups with a placebo group and the group ratios. The Bonferroni correction and the plug-in method based on the multivariate-t distribution have been proposed for the simultaneous region estimation. However, the two methods are asymptotic procedures, and their performance in finite sample sizes has not been thoroughly investigated. Based on the concept of generalized pivotal quantity, we propose a Bonferroni correction procedure and a generalized variable (GV) procedure to construct the simultaneous confidence regions. To address a genetic concern of the dominance ratio, we conduct a simulation study to empirically investigate the probability coverage and expected length of the methods for various combinations of sample sizes and values of the dominance ratio. The simulation results demonstrate that the simultaneous confidence region based on the GV procedure provides sufficient coverage probability and reasonable expected length. Thus, it can be recommended in practice. Numerical examples using published data sets illustrate the proposed methods.     

Estimation of P{X < Y} for geometric—exponential model based on complete and censored samples

This article deals with the estimation of R = P{X < Y}, where X and Y are independent random variables from geometric and exponential distribution, respectively. For complete samples, the MLE of R, its asymptotic distribution, and confidence interval based on it are obtained. The procedure for deriving bootstrap-p confidence interval is presented. The UMVUE of R and UMVUE of its variance are derived. The Bayes estimator of R is investigated and its Lindley's approximation is obtained. A simulation study is performed in order to compare these estimators. Finally, all point estimators for right censored sample from the exponential distribution, are obtained.