On using influence functions for testing multivariate normality

Changes in the joint distribution of influence functions for the mean vector and the covariance matrix are examined when the true probability distribution is contaminated. In particular, the formulas for influence functions of the first and second moments with respect to the above joint distribution are obtained and used to derive reasonable test statistics for multivariate normality. The formulas are extended by using the joint distribution of score functions for population parameters. An application of the extended formulas to the usual linear regression analysis leads to a measure of multivariate skewness which can be used to reduce the effect of non-normality of the response variable. Also, some relationship between the extended formulas and goodness-of-fit statistics is discussed and used to derive test statistics for multivariate normality.     

Ion-pair high-performance liquid chromatography separation of β-endorphin-(6–17) from fourteen fragments

Summary In order to support metabolism studies of the proposed antipsychotic compound β-endorphin-(6–17), (Org 5878), the HPLC separation of this parent compound from fourteen peptide fragments was studied. The addition to the mobile phase of hydrophobic ion-pairing agents proved to be necessary to obtain adequate separation. The influence of the chromatographic parameters pH, type and concentration of the pairing agent, buffer concentration and temperature were investigated systematically. As a result the complete separation of Org 5878 and its fourteen fragments is reported.     

An imputation method for dealing with missing data in regression

We develop two methods for imputing missing values in regression situations. We examine the standard fixed-effects linear-regression model Y = X β + ?, where the regressors X are fixed and ? is the error term. This research focuses on the problem of missing X values. A particular component of market-share analysis has motivated this research where the price and other promotional instruments of each brand are allowed to have their own impact on the total sales volume in a consumer-products category. When a brand is not distributed in a particular week, only a few of the many measures occurring in that observation are missing. ‘What values should be imputed for the missing measures?’ is the central question this paper addresses. This context creates a unique problem in the missing-data literature, i.e. there is no true value for the missing measure. Using influence functions, from robust statistics we develop two loss functions, each of which is a function of the missing and existing X values. These loss functions turn out to be sums of ratios of low-order polynomials. The minimization of either loss function is an unconstrained non-linear-optimization problem. The solution to this non-linear optimization leads to imputed values that have minimal influence on the estimates of the parameters of the regression model. Estimates using the method for replacing missing values are compared with estimates obtained via some conventional methods.     

Effect of the initial estimator on the asymptotic behavior of one-step M-estimator

For a general (real) parameter, let M _nbe the M-estimator and M _n ⁽¹⁾ be its one-step version (based on a suitable initial estimator M _n ⁽⁰⁾). It is known that, under certain regularity conditions, n(M _n ⁽¹⁾-M _n)=O _p(1). The asymptotic distribution of n(M _n ⁽¹⁾-M _n) is studied; it is typically non-normal and it reveals the role of the initial estimator M _n ⁽⁰⁾.Work of this author was partially supported by the Office of Naval Research, Contract No. N00014-83-K-0387     

强磁场等离子体中电子的弛豫时间

用考虑磁场对碰撞影响所得的几率分布动力学方程,研究了磁场高达10~8T,密度10~(26)—10~(27)cm~(-3),温度10keV情况下的电子弛豫过程,计算了弛豫时间,并与不考虑磁场对碰撞影响时的结果进行了比较。     

Arai实测谱分布数据的应用

对Arai的靶原级谱分布数据 ,通过插值、拟合处理 ,获得适用于数值积分的Δλ =0 0 0 2nm的谱分布数据 ,建立了新的谱分布数据文件 ,应用于FPM程序中。并对耐热钢GH131进行实验研究。理论强度与测量强度的相关性良好 ;基本参数法与理论影响系数法分析结果与确认值一致 ,对Cr,Ni分析的相对误差 <1 0 %。结果表明 :经处理的Arai的靶原级谱分布数据应用于FPM程序 ,提高了分析准确性 ,并扩大了基本参数法与理论影响系数法的应用范围。     

Die Wahl der Trägergasgeschwindigkeit bei der Analyse von Mehrkomponenten-Gemischen

Zusammenfassung Die Wahl der mittleren, linearen Tr?gergasgeschwindigkeit bei der Analyse von Mehrkomponentengemischen unter isothermen und temperaturprogrammierten Bedingungen wird diskutiert. Es wird gezeigt, da? stets eine Tr?gergasgeschwindigkeit gew?hlt werden sollte, die mindestens gleich, besser jedoch h?her ist, als die optimale Gasgeschwindigkeit für den ersten Peak, gemessen bei der Starttemperatur (Temperaturprogramm) oder bei der eingestellten Ofentemperatur (isotherme Fahrweise).

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You can read this article in English in issue 12, 509 (1979).     

Influence of lanthanum on the performance of Zr-Co/activated carbon catalysts in Fischer-Tropsch synthesis

The influence of La loading on Zr-Co/activated carbon （AC） catalysts has been studied for Fischer-Tropsch synthesis. The catalyst samples were characterized by XRD, TPR, CO-TPD, and temperature programmed CO hydrogenation. The catalytic property was evaluated in a fixed bed reactor. The experimental results showed that CO conversion increased from 86.4% to 92.3% and the selectivity to methane decreased from 14.2% to 11.5% and C5＋ selectivity increased from 71.0% to 74.7% when low La loading （La = 0.2wt%） was added into the Zr-Co/AC catalyst. However, high loadings of La （La = 0.3-1.0 wt%） would decrease catalyst activity as well as the C5＋ selectivity and increase methane selectivity. XRD results displayed that La-modified Zr-Co/AC catalyst had little effect on the dispersion of Co catalyst. But, the results of TPR, CO-TPD, and temperature programmed CO hydrogenation techniques indicated that the extent of cobalt reduction was found to greatly influence the activity and selectivity of the catalyst. The addition of a small amount of La increased the reducibility of the Zr-Co/AC catalyst and restrained the formation of methane and improved the selectivity to long chain hydrocarbons. However, excess of La led to the decrease of the reducibility of Co catalyst thus resulted in higher methanation activity.     

创新型企业的空间集聚及影响因素分析

以福建省创新型企业为例,研究分析创新型企业的空间格局特征,以及创新型企业建设与地区经济发展之间的关系.根据区位基尼系数探讨创新型企业的集聚特征.利用Moran指数与Moran散点图,分析创新型企业数量分布的全局空间自相关性与局部空间自相关性.研究表明:创新型企业的建设成效与地区经济发展水平之间呈高度正相关关系;创新型企业的建设在地区内部辐射作用强,对邻近地区正溢出效应弱,甚至产生负溢出效应.