Bootstrap approach to test the homogeneity of order restricted mean vectors when the covariance matrices are unknown

Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are unknown, arbitrary positive definite and unequal are considered. This problem of testing has been studied to some extent, for example, by Kulatunga and Sasabuchi (1984 Kulatunga, D. D. S., Sasabuchi, S. (1984). A test of homogeneity of mean vectors against multivariate isotonic alternatives. Mem Fac Sci, Kyushu Univ Ser A Mathemat 38:151–161. [Google Scholar]) when the covariance matrices are known and also Sasabuchi et al. (2003 Sasabuchi, S., Tanaka, K., Tsukamodo, T. (2003). Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown. Annals of Statistics. 31(5):1517–1536.[Web of Science ®] , [Google Scholar]) and Sasabuchi (2007 Sasabuchi, S. (2007). More powerful tests for homogeneity of multivariate normal mean vectors under an order restriction. Sankhya 69(4):700–716. [Google Scholar]) when the covariance matrices are unknown but common. In this paper, a test statistic is proposed and because of the main advantage of the bootstrap test is that it avoids the derivation of the complex null distribution analytically, a bootstrap test statistic is derived and since the proposed test statistic is location invariance the bootstrap p-value defined logical and some steps are presented to estimate it. Our numerical studies via Monte Carlo simulation show that the proposed bootstrap test can correctly control the type I error rates. The power of the test for some of the p-dimensional normal distributions is computed by Monte Carlo simulation. Also, the null distribution of test statistic is estimated using kernel density. Finally, the bootstrap test is illustrated using a real data.     

The beta skew-generalized normal distribution

In this article, we develop the skew-generalized normal distribution introduced by Arellano-Valle et al. (2004 Arellano-Valle, R.B., Gomez, H.W., Quintana, F.A. (2004). A new class of skew-normal distribution. Commun. Stat. - Theory Methods. 33(7):1465–1480.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) to a new family of the Beta skew-generalized normal (BSGN) distribution . Here, we present some theorems and properties of BSGN distribution and obtain its moment-generating function.     

An integral formula for the distribution of self-normalized Gaussian random samples

Given i.i.d. Gaussian random variables and after standardizing the sample by subtracting the sample mean and dividing it by the sample deviation, we obtain an integral formula for the distribution of these self-normalized variables. Using geometrical arguments, we obtain the distribution of each and the joint distribution of two of them. These formulas can be used to calculate the expected value of the particular type of Cramér von Mises statistic to test normality.     

Bayesian expectile regression with asymmetric normal distribution

In this paper, we adopt the Bayesian approach to expectile regression employing a likelihood function that is based on an asymmetric normal distribution. We demonstrate that improper uniform priors for the unknown model parameters yield a proper joint posterior. Three simulated data sets were generated to evaluate the proposed method which show that Bayesian expectile regression performs well and has different characteristics comparing with Bayesian quantile regression. We also apply this approach into two real data analysis.     

Household gambling expenditures and the Irish recession

This article examines the determinants of household gambling expenditures in Ireland and the effects of the recession on these expenditures using a large micro data-set, the Irish Household Budget Survey (HBS). Two gambling expenditures are examined, bookmaker tote betting and spending on the national lottery. Households with an older and a less educated head of household participate in and spend more on both forms of gambling while the presence of children in the households tends to reduce participation and spending in gambling. There is also evidence to suggest that households with an unemployed head of household have a higher likelihood of participation in gambling. The recession has affected the two forms of gambling in different ways. Lottery expenditures appear resilient to the effects of the recession. This is demonstrated in the estimated expenditure elasticities in particular. Bookmaker/tote expenditures have changed from a necessity to a luxury good, while lottery expenditures have increased in their necessity status. This can be explained by the fact that playing the lottery requires less time, knowledge and risk and has potentially greater benefits attached to it in comparison to bookmaker/tote betting. During a recession these factors become much more prevalent.     

新课改背景下数学师范生专业技能培养的探究

介绍新课改对数学教师的新要求,设想数学师范生专业技能的结构,并对数学师范生专业技能的培养原则及其措施进行了探究.     

文化自觉：照亮中国基础教育理性化阴影之灯

中国传统基础教育以私塾为形式,人文性的四书五经为其内容。清末民初,私塾为理性化的班级授课制所取代,这是理性在教育领域的第一次胜利;近十年来,基础教育集中于乡镇以上学校,村小学被拆并,乡镇初中日渐缩减,农村教育资源被抽空,这是理性在教育领域的进一步扩张。理性化带有形式合理而实质不合理的悖论特质。基础教育之理性化带来高效益的同时,也导致文化意识与价值观念越来越淡漠。目前,较为富强的中国社会也越发意识到,文化归宿之于中国人安身立命以及社会的可持续发展的价值所在。克服教育理性化阴影,在于文化的再植入。故而,面对教育理性化,亟待嵌入文化意识,须将本土文化嵌入基础教育之中以避免教育的无根性。     

我国供给侧结构性改革研究

推进供给侧结构性改革是我国为适应经济发展新阶段所提出的创新举措,一方面是转变经济发展方式,跨越"中等收入陷阱"的主动选择,另一方面是全面深化改革,全面建成小康社会的必然要求。"十三五"时期是经济结构调整的关键时期,当前中国经济面临的主要矛盾由需求侧转向供给侧,面临体制性、结构性矛盾,必须减少无效供给,增加有效供给,增强经济发展动力,为经济持续健康发展创造条件。     

新常态视角下高校社会服务功能拓展研究

高校社会服务功能拓展是经济"新常态"背景下的应有之义和必然选择。强化高校社会服务的职能观,以社会需求为导向培养应用型人才,面向社会领域主动开展科学研究,构建高校科学研究转化机制,建立高校社会服务的激励与评价机制,是高校社会服务主动适应和服务"新常态"的重要举措。     

"科技-生产"范式的内涵及其历史演进

"科学、技术、生产"所组成的紧密联系的整体构成了"科技-生产"系统,这一系统的内在结构关系表现为某种模式、模型,它是科学、技术、生产三者相互作用关系的集中体现.我们将这一模式、模型称为"科技-生产"范式.思维模式规定性、技术规定性、制度规定性、结构功能规定性是"科技-生产"范式的四种基本属性.人类历史迄今,"科技-生产"范式经历了一系列转换,包括"实体-能量-信息"三重思维模式转换、从"革命-延续"到"创新-集成"的技术转换、"强制有序-协同自序"制度体系的转化以及"工业社会-知识社会"的结构功能转换等.积极促进我国"科技-生产"范式的转换,建立新型的"科技-生产"范式对于新型工业化社会的构建具有重要意义.