On Sharp Jensen's Inequality and Some Unusual Applications

The purpose of this article is two-fold. First, we find it very interesting to explore a kind of notion of optimality of the customary Jensen-bound among all Jensen-type bounds. Without this result, the customary Jensen-bound stood alone simply as just another bound. The proposed notion and the associated optimality are important given that in some situations the Jensen's inequality does leave us empty handed.

When it comes to highlighting Jensen's inequality, unfortunately only a handful of nearly routine applications continues to recycle time after time. Such encounters rarely produce any excitement. This article may change that outlook given its second underlying purpose, which is to introduce a variety of unusual applications of Jensen's inequality. The collection of our important and useful applications and their derivations are new.     

经济增速放缓与经济波动对居民福利影响的阶段差异分析

 本文基于中国1952-2007年时序数据定量研究经济增速放缓的福利损失和经济波动的福利损失,并侧重考察两种福利损失的大小关系在改革开放和经济体制改革目标确立前后的阶段差异。研究发现,无论是总体而言,还是在中国经济发展的不同阶段,经济波动的福利损失并不必然远小于经济增速放缓的福利损失,在相关参数的合理取值范围内,经济波动的福利损失大于经济增速放缓的福利损失是相当普遍的情形。因此,中国政府部门在重视长期经济增长的同时,不能草率否定短期经济稳定的重要性。     

Interval Estimation for the Difference of Two Independent Variances

Analytical methods for interval estimation of differences between variances have not been described. A simple analytical method is given for interval estimation of the difference between variances of two independent samples. It is shown, using simulations, that confidence intervals generated with this method have close to nominal coverage even when sample sizes are small and unequal and observations are highly skewed and leptokurtic, provided the difference in variances is not very large. The method is also adapted for testing the hypothesis of no difference between variances. The test is robust but slightly less powerful than Bonett's test with small samples.     

On Statistics Independent of a Sufficient Statistic: Basu's Lemma

The determination of optimal sample sizes for estimating the difference between population means to a desired degree of confidence and precision is a question of economic significance. This question, however, is generally not discussed in statistics texts. Sample sizes to minimize linear sampling costs are proportional to the population standard deviations and inversely proportional to the square roots of the unit sampling costs. Sensitivity analysis shows that the impact of the use of equal rather than optimal sample sizes on the amount of sampling and its cost is not great as long as the unit costs and population variances are comparable.     

对大学“素质教育”教学原则的探析及论证

“素质教育”作为一种教育理论已风靡全国,甚至有对世界教育理论产生重大影响之势。该文从探讨“素质教育”的重要支撑教学原则的角度出发,以社会发展和人的发展的客观规律为依据,提出并论证了“强化主体性”等四条素质教育的教学基本原则,并对教学原则的实施提出了相应的教改思路     

“大分流”的文化成因说评析

美国学者格里高利·克拉克把工业革命后英国等西方国家的崛起,和中国等亚非国家的持续落后所形成的所谓大分流,归因于所谓文化因素,即不同国家的文化背景决定了各国劳动者的劳动态度和企业管理水平,而劳动态度和管理水平则决定了劳动效率,从而决定了各国经济的不同走向和发展水平。他在进行中国和英美比较时使用了1910年棉纺织业劳动力使用效率作为证据。事实上,他把机器棉纺织工业刚起步不久的中国与工业革命已开展100多年的英美作静态比较,并得出文化差异的结论,是不合理的。在1910年以后的二三十年中,中国机器棉纺织业劳动力使用效率有明显的提升,提升的原因有企业管理制度的改革、管理人员专业化程度的提高、工人职业培训的加强、工人自治制度的实施等;但负面的制约因素持续存在,如货币和经济的大幅波动、社会和政治局势的动荡、国民教育水平提升缓慢、社会保障制度没有建立等。这些有待于国家的全面转型。这些正面和负面的因素说明:随着企业制度和社会制度的改进,劳动效率就会不断提高。文化差异并不妨碍制度改进。大分流的文化成因说很难成立。     

农村儿子、女儿对父母的经济支持差异研究

利用2010年中国人民大学组织的家庭及生育状况研究调查数据,采用固定效应的Logistic模型和多元回归模型,研究农村儿子、女儿对父母的经济支持差异。结果发现,尽管农村中女儿比儿子更有可能对老人进行正向经济支持,但在对父母进行正向经济支持的人中,儿子对老人的经济支持力度仍然比女儿大。在控制了一系列微观个体特征、中观家庭特征和宏观区域特征后,对老人的经济支持力度的性别差异越发明显。在我国农村,儿子对父母的经济支持力度仍然显著强于女儿。     

Classification of difference matrices over cyclic groups

The existence of difference matrices over small cyclic groups is investigated in this computer-aided work. The maximum values of the parameters for which difference matrices exist as well as the number of inequivalent difference matrices in each case is determined up to the computational limit. Several new difference matrices have been found in this manner. The maximum number of rows is 9 for an r ×15 difference matrix over Z₃, 8 for an r ×15 difference matrix over Z₅, and 6 for an r ×12 difference matrix over Z₆; the number of inequivalent matrices with these parameters is 5, 2, and 7, respectively.     

价格持续期的SEMIFAR-ACD模型

本文提出了一类同时包含确定性,差分平稳以及平稳长相关趋势的描述交易价格持续期新模型---SEMIFAR-ACD模型。研究了模型的估计方法和各估计量的渐近性质,构建了相应的估计算法,并应用实际数据,将SEMIFAR-ACD模型与普通ACD模型模拟效果进行比较,论证了SEMIFAR-ACD模型更好的描述数据的性能。