超声提取-反相高效液相色谱法测定棉仁中游离棉酚

用超声提取对棉仁进行预处理,探讨了影响棉酚提取率的因素,确定其最佳提取条件为:料液比0.1∶15(g/mL),提取时间50min,超声功率90W。在最佳提取条件下,棉仁中游离棉酚的平均提取率为6.3282 mg/g。利用反相高效液相色谱(RP-HPLC)法测定棉仁中游离棉酚含量,使用SinoChrom ODS-BP C18色谱柱(200×4.6mm,5μm),流动相为甲醇-1%磷酸水溶液(体积比85∶15),流速为0.9mL/min,紫外检测波长为238nm。结果表明,棉酚在0.0044～0.0352mg/mL范围内与色谱峰面积呈良好线性关系,线性相关系数为0.9998,平均加标回收率在98.80%～99.03%之间。该法快速、灵敏、准确,适用于棉仁中游离棉酚的定量分析。     

一种用于土壤非金属养分测试的光纤探头式分光光度计

针对测土配方施肥技术中要求快速、便捷、高效地进行土壤养分测试的需求,文章基于浸入式光纤探头、平场凹面全息光栅、二极管线阵检测器开发了一种光纤探头式分光光度计用于土壤养分中非金属元素的快速、准确测试。基于国家计量检定规程JJG 178—2007对紫外、可见、近红外分光光度计的性能检测方法测试的该仪器的波长最大允许误差与波长重复性、基线平直度、透射比最大允许误差与透射比重复性均达到了国标第Ⅲ级别标准,其最小光谱带宽、噪声与漂移、杂散光基本达到了国标第Ⅳ级别标准。基于该仪器测试的土壤硝态氮、铵态氮、有效磷、有效硫、有效硼、和有机质含量与基于商用的国产单光束和进口双光束分光光度计测试的结果呈极显著的线性相关关系,其回归方程的斜率接近于1,且对比数据之间无显著性差异。因此,该光纤探头式分光光度计可用于土壤非金属养分的快速、准确测试。     

Empirical likelihood for AR-ARCH models based on LAD estimation

By employing the empirical likelihood method,confidence regions for the stationary AR(p)-ARCH(q) models are constructed.A self-weighted LAD estimator is proposed under weak moment conditions.An empirical log-likelihood ratio statistic is derived and its asymptotic distribution is obtained.Simulation studies show that the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy,especially for relative small size of observation.     

The block sphericity test—exact and near‐exact distributions for the likelihood ratio statistic

Using a suitable decomposition of the null hypothesis of the sphericity test for several blocks of variables, into a sequence of conditionally independent null hypotheses, we show that it is possible to obtain the expressions for the likelihood ratio test statistic, for its hth null moment, and for the characteristic function of its logarithm. The exact distribution of the logarithm of the likelihood ratio test statistic is obtained in the form of a sum of a generalized integer gamma distribution with the sum of a given number of independent logbeta distributions, taking the form of a single generalized integer gamma distribution when each set of variables has two variables. The development of near‐exact distributions arises, from the previous decomposition of the null hypothesis and from the consequent‐induced factorization of the characteristic function, as a natural and practical way to approximate the exact distribution of the test statistic. A measure based on the exact and approximating characteristic functions, which gives an upper bound on the distance between the corresponding distribution functions, is used to assess the quality of the near‐exact distributions proposed and to compare them with an asymptotic approximation on the basis of Box's method. Copyright © 2011 John Wiley & Sons, Ltd.     

Prior influence in linear regression when the number of covariates increases to infinity

It is becoming more typical in regression problems today to have the situation where “p>n”, that is, where the number of covariates is greater than the number of observations. Approaches to this problem include such strategies as model selection and dimension reduction, and, of course, a Bayesian approach. However, the discrepancy between p and n can be so large, especially in genomic data, that examining the limiting case where p→∞ can be a relevant calculation. Here we look at the effect of a prior distribution on the coefficients, and in particular characterize the conditions under which, as p→∞, the prior does not overwhelm the data. Specifically, we find that the prior variance on the growing number of covariates must approach zero at rate 1/p, otherwise the prior will overwhelm the data and the posterior distribution of the regression coefficient will equal the prior distribution.     

非线性回归模型的经验似然诊断

经验似然方法已经被广泛用于线性模型和广义线性模型.本文基于经验似然方法对非线性回归模型进行统计诊断.首先得到模型参数的极大经验似然估计;其次基于经验似然研究了三种不同的影响曲率度量;最后通过一个实际例子,说明了诊断方法的有效性.     

分数填补下两总体分位数差异的经验似然置信区间

设有两个非参数总体,其样本数据不完全,用分数填补法补足缺失数据,得到两总体的"完全"样本数据,在此基础上构造两总体分位数差异的经验似然置信区间.模拟结果显示,分数填补法可以得到更加精确的置信区间.     

Relative entropy and large deviations under sublinear expectations

We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.     

非对称损失函数下Burr Ⅻ型分布可靠性指标的Bayes估计

本文研究了R=P(Y＜X)在两种非对称损失函数下的Bayes估计问题,其中随机变量X和Y相互独立且服从不同的Burr XII型分布.利用Lindley近似方法,获得了Bayes估计的显式近似表达式,通过随机模拟比较了不同损失函数下的Bayes估计的性质.