Diagnostic tests for the distribution of random effects in multivariate mixed effects models

Abstract

Fourier methods are proposed for testing the distribution of random effects in classical and robust multivariate mixed effects models. The test statistics involve estimation of the characteristic function of random effects. Theoretical and computational issues are addressed while Monte Carlo results show that the new procedures compare favorably with other methods.     

An Introduction to Ranking and Selection

This expository paper explains the philosophy of the indifference-zone approach and the subset-selection approach to ranking and selection procedures. It includes examples of operating characteristic curves and data applications for selection problems based on the binomial and normal distributions. A variety of different models and goals are provided with a list of references.     

论历史自信的历史生成与时代遵循

坚定历史自信,增强历史主动,事关党和国家事业行稳致远,事关中华民族伟大复兴。历史自信,既是党的百年奋斗光辉历程的历史展开过程,也是中华民族伟大复兴历史进程中凝聚奋斗力量、形成历史伟力的精神力量。在新的赶考之路上坚定历史自信,要以学懂、弄通、做实《中共中央关于党的百年奋斗重大成就和历史经验的决议》的精神为根本遵循,以弘扬伟大精神为思想动力,以坚持科学的唯物史观为基本方法,以淬炼党性修养为关键路径。     

“两个确立”视域下中国式现代化的历史自信与文化自信

〗“两个确立”为中国式现代化提供了根本保证。以中国式现代化推动中华民族伟大复兴,必须坚持中国共产党的全面领导,全面贯彻落实习近平新时代中国特色社会主义思想。“两个确立”坚定了中国式现代化的历史自信。新时代十年的伟大变革和历史性成就,充分证明中国式现代化顺应了社会历史发展的客观规律,是历史和人民的正确选择。“两个确立”增强了中国式现代化的文化自信,坚持了马克思主义现代化理论,弘扬了中华优秀传统文化,借鉴和吸收了人类文明优秀成果,开创了人类文明新形态。     

Characteristic Function‐based Semiparametric Inference for Skew‐symmetric Models

Skew‐symmetric models offer a very flexible class of distributions for modelling data. These distributions can also be viewed as selection models for the symmetric component of the specified skew‐symmetric distribution. The estimation of the location and scale parameters corresponding to the symmetric component is considered here, with the symmetric component known. Emphasis is placed on using the empirical characteristic function to estimate these parameters. This is made possible by an invariance property of the skew‐symmetric family of distributions, namely that even transformations of random variables that are skew‐symmetric have a distribution only depending on the symmetric density. A distance metric between the real components of the empirical and true characteristic functions is minimized to obtain the estimators. The method is semiparametric, in that the symmetric component is specified, but the skewing function is assumed unknown. Furthermore, the methodology is extended to hypothesis testing. Two tests for a null hypothesis of specific parameter values are considered, as well as a test for the hypothesis that the symmetric component has a specific parametric form. A resampling algorithm is described for practical implementation of these tests. The outcomes of various numerical experiments are presented.     

Testing for spherical symmetry via the empirical characteristic function

Kolmogorov–Smirnov-type and Cramér–von Mises-type goodness-of-fit tests are proposed for the null hypothesis that the distribution of a random vector X is spherically symmetric. The test statistics utilize the fact that X has a spherical symmetric distribution if, and only if, the characteristic function of X is constant over surfaces of spheres centred at the origin. Both tests come in convenient forms that are straightforwardly applicable with the computer. The asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions. Since both the finite sample and the asymptotic null distribution depend on the unknown distribution of the Euclidean norm of X, a conditional Monte Carlo procedure is used to actually carry out the tests. Results on the behaviour of the test in finite-samples are included along with a real-data example.     

历史解释与历史重演——重塑《左传·郑伯克段于鄢》中郑庄公的形象

《左传·郑伯克段于鄢》是非常著名的历史叙述文本,讲述了庄公兄弟二人为王位而反目成仇的过程。《左传》评价"兄不友、弟不恭"的伦常失序是事件的起因。后世评论多以此为据,而忽视兄弟二人的母亲武姜的政治力量。清华简第六辑《郑武夫人规孺子》,塑造出颇具政治谋略的武姜,综合《左传·郑伯克段于鄢》的叙述,借助历史重演解释理论分析可知,她与庄公多年秘而不宣的政治角力,是郑伯克段叙述中的内隐的政治背景。庄公借助边父、祭仲等人的长久筹谋,因势利导,驱逐共叔段、拘禁武姜,避免郑国内乱,为国家兴盛谋求发展空间,但他养骄长恶,一贯以满足个体私欲来豢养王室及其近属,为郑国埋下内乱的祸根。     

现代化新路

十九大报告中,习近平总书记提出了新时代中国特色社会主义思想这一全新命题。该命题是对马克思主义的继承和发展,是对中国特色社会主义道路自信、理论自信、制度自信和文化自信的当代诠释,为中国特色社会主义的发展、为发展中国家如何进行现代化建设开辟了新的路径。具体来说,习近平新时代中国特色社会主义思想有着深厚的历史意义,它不仅促进马克思主义在21世纪的复兴,为处于低谷的国际共产主义运动提供了动力,在共建中共享,为世界和平发展贡献了中国方案和中国智慧,而且开辟了现代化发展的新路向,为发展中国家如何发展提供了镜鉴。