Testing for normality in linear regression models

The importance of the normal distribution for fitting continuous data is well known. However, in many practical situations data distribution departs from normality. For example, the sample skewness and the sample kurtosis are far away from 0 and 3, respectively, which are nice properties of normal distributions. So, it is important to have formal tests of normality against any alternative. D'Agostino et al. [A suggestion for using powerful and informative tests of normality, Am. Statist. 44 (1990), pp. 316–321] review four procedures Z ²(g ₁), Z ²(g ₂), D and K ² for testing departure from normality. The first two of these procedures are tests of normality against departure due to skewness and kurtosis, respectively. The other two tests are omnibus tests. An alternative to the normal distribution is a class of skew-normal distributions (see [A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171–178]). In this paper, we obtain a score test (W) and a likelihood ratio test (LR) of goodness of fit of the normal regression model against the skew-normal family of regression models. It turns out that the score test is based on the sample skewness and is of very simple form. The performance of these six procedures, in terms of size and power, are compared using simulations. The level properties of the three statistics LR, W and Z ²(g ₁) are similar and close to the nominal level for moderate to large sample sizes. Also, their power properties are similar for small departure from normality due to skewness (γ₁≤0.4). Of these, the score test statistic has a very simple form and computationally much simpler than the other two statistics. The LR statistic, in general, has highest power, although it is computationally much complex as it requires estimates of the parameters under the normal model as well as those under the skew-normal model. So, the score test may be used to test for normality against small departure from normality due to skewness. Otherwise, the likelihood ratio statistic LR should be used as it detects general departure from normality (due to both skewness and kurtosis) with, in general, largest power.     

基于GARCHSK的铜期货VaR估计方法研究

基于GARCHSK模型对期货收益序列的条件偏度和峰度进行动态建模,提出了“有偏”和“尖峰厚尾”分布下的VaR估计方法。通过对沪铜期货的实证研究表明,其收益分布存在明显的“有偏”和“尖峰厚尾”。基于不同分布假定下的VaR估计结果的Kupiec检验表明,基于GARCHSK的VaR估计方法能够有效提高VaR的估计精度。     

Natural (Non‐)Informative Priors for Skew‐symmetric Distributions

In this paper, we present an innovative method for constructing proper priors for the skewness (shape) parameter in the skew‐symmetric family of distributions. The proposed method is based on assigning a prior distribution on the perturbation effect of the shape parameter, which is quantified in terms of the total variation distance. We discuss strategies to translate prior beliefs about the asymmetry of the data into an informative prior distribution of this class. We show via a Monte Carlo simulation study that our non‐informative priors induce posterior distributions with good frequentist properties, similar to those of the Jeffreys prior. Our informative priors yield better results than their competitors from the literature. We also propose a scale‐invariant and location‐invariant prior structure for models with unknown location and scale parameters and provide sufficient conditions for the propriety of the corresponding posterior distribution. Illustrative examples are presented using simulated and real data.     

硅胶基吸附材料的合成方法

硅胶基吸附材料是以硅胶为基质合成的一种对金属离子具有良好吸附性能的材料．本文从改性机理和合成路径两方面综述了硅胶基吸附材料的合成方法,并讨论了不同合成路径（异相法、均相法、共聚法）的优缺点．     

“十二五” 规划中“包容性增长”概念探析

“包容性增长”包括经济、政治、文化、社会、生态等各个方面,经济增长与其他各方面的增长应该是互相协调、和谐增长、可持续增长和科学增长;经济增长的同时,财富公平分配,不造成贫富差距,向低收入人群倾斜,使所有人都从增长中获益。文章旨在通过对“包容性增长”概念之阐释,以更好地理解“包容性增长”的深刻含义,促进经济变革与社会更好更快地发展。     

我国股票市场收益率偏度对风险补偿的影响研究

收益率与波动率之间的关系(风险补偿)在金融资产定价和风险管理中至关重要,但二者之间的研究却一直没有定论。金融理论表明为正向关系,但实证却往往得到相反的结果。众所周知,尖峰厚尾以及负偏是收益率的典型特性。这些内在属性对风险补偿无疑有着重要的影响。本文研究表明,收益率的负偏和尖峰厚尾会导致风险补偿系数减小,进而导致风险补偿系数在实证当中的不确定性。虽然各个行业的夏普比率相差无几,我国股票市场的第“I”类、第“II”类风险补偿以及风险价格在不同行业之间存在较大的差异,且三者随着投资期限的增长,分别有下降、上升和轻微上升的趋势。     

具有Neumann边值的齐次p-Laplacian方程的指标分类理论

通过建立指标分类理论讨论了一维p-Laplacian方程(φp(u′))′+q(t)φp(u)=0,a.e on[0,1]在Neumann边值u′(0)=0=u′(1)条件下平凡解和非平凡解的存在性,其中φp(s)=s p-2s,p>1,q∈L∞(0,1)。     

三阶线性齐次微分方程解的Sturm比较定理

研究了一类三阶线性齐次微分方程解的Sturm比较定理的理论,在三阶线性齐次微分方程的Sturm基本定理的基础上得出了Sturm比较定理,所得结论推广了现有文献的相应结果。     

私人刑事调查与侦查之比较

私人刑事调查作为自我保护与私力救济的重要手段,它同侦查存在着紧密联系。经过分析比较发现,一方面私人刑事调查与侦查有着明显同质性,这多涵盖最终目的、历史起源和启用手段种类三部分。另一方面它们二者又存在明显异质性,这主要包括基本性质、实施主体、启用手段比重、直接目的、运作范围、具体程序及受众心理七方面。