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双语推荐：广义岭估计

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对有偏估计中的广义岭型主成分估计的优良性进行了较深入的研究。证明了广义岭型主成分估计优于最小二乘估计的充要条件，并在此基础上对几类常见的有偏估计在均方误差（阵）条件下优于最小二乘估计的充要条件进行了拓展。
In the paper , the choiceness of the generalized ridge principal component estimation in biased estimation was studied .In the process, the necessary and sufficient condition that the generalized ridge principal component estimation is superior to least square estimation was proved .In the light of this demonstration , the necessary and sufficient condition of a few common biased estimations was expanded , that is, they are superior to least square estimation under the condition of mean square error .

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基于线性回归模型参数向量的先验信息提出一类新的s-K估计——改进s-K估计,并在均方误差阵意义下,得到了这类估计分别优于最小二乘估计、广义岭估计、Stein估计及s-K估计的充要条件.
A new class of s-K estimators,called the modified s-K estimators was proposed based on the prior information for the parameter vector in a linear model. The necessary and sufficient conditions that the new estimators are respectively superior to the least squares estimator,ridge estimators,Stein estimators and s-K estimators were obtained.

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针对Gauss-Markov模型,讨论了在均方误差矩阵(MSEM)准则和Pitman Closeness(PC)准则下回归系数的广义岭估计相对于最小二乘估计的优良性.
For the Gauss-Markov model,under the mean square error matrix(MSEM)criterion and Pitman Closeness (PC)criterion,the superiorities of the generalized ridge estimator of regression coefficients over the least square estimator were studied.

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通过参数Bootstrap方法和广义推断方法得到了两正态分布总体变异系数差的区间估计,并通过模拟计算比较两种方法的优劣.利用Bootstrap方法,得到了参数Bootstrap样本,计算两总体变异系数差的区间估计;采用广义区间估计法,分别构造两个正态分布总体变异系数的广义枢轴量,求解两正态分布总体变异系数差的区间估计,最后通过模拟计算比较两种区间估计.研究结果表明,广义推断法能够更好地进行区间估计.
This article proposed parameter Bootstrap method and generalized inference method to study the confidence interval of the comparison of variation coefficients for two normal distributions ,respec-tively .Then we compared two methods by simulation study .Parameter Bootstrap method was proposed for computing the coefficient of variations of two normal distributions .And according to generalized in-terval estimation method ,we constructed the generalized pivot quantity of the two normal distributions variation coefficient ,then two normal distribution coefficient of variation .Finally ,the simulation study for comparing two interval estimations was given .The research result indicated that the generalized in-ference method was a better interval estimation method .

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重要结论：1.事故频次数据样本量对预测精度影响很大；2.广义估计方程能够有效考虑事故频次数据中存在的时间相关性；3.广义估计方程的参数估计比传统广义线性模型更准确，且精度更高。
Traditional crash frequency modeling uses crash frequency data averaged across multiple years. When data size is small, crash data in each year are used in the modeling to extend the size of the samples. The extension of sample size could create a temporal correlation among crash frequencies of the different years, which could affect the modeling accuracy. The primary objective of this study is to evaluate the application of the generalized estimating equation (GEE) procedures to account for the temporal correlation in the longitudinal crash frequency data. Four-year crash data at exit ramps on a freeway in China were collected for modeling. Based on the same data, traditional generalized linear models (GLMs) were estimated for model com-parison. Results showed that traditional GLM underestimated the standard errors of coefficients for explanatory variables. The GEE procedure with an exchangeable correlation structure successively captured the temporal correlation among the crash fre-q

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引进二元广义Baskakov算子逼近的余项定义,并针对三类不同函数的余项给出了的三种估计形式,推广了一元广义Baskakov算子逼近的余项估计结果,同时改进了二元广义Baskakov算子逼近度的定理.
The definition of approximated remainders with two-dimensional generalized Baskakov operators is introduced , the remainders are discussed for three kinds of functions , and three forms of estimated remainders are obtained . The results of remainder estimation of approximation by generalized Baskakov operator are extended , and the theorems of approximation degree of two-dimensional generalized Baskakov operators are improved , so that the results become even more precisely .

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考虑偶数阶微分方程在Dirichlet和Neumann边界条件下广义特征值的估计,利用方程特征值理论、分部积分、测试函数、广义Rayleigh定理和不等式估计等方法,获得了主次特征值之比的下界估计不等式,且估计值与区间的几何量无关.
This paper presents the generalized eigenvalue estimate for even - order differential equation under the Neumann boundary condition as well as Dirichlet. The inequality of the lower bound of the ratio of princi-pal eigenvalue to secondary eigenvalue is estimated by using eigenvalue theory of equation,integration by parts,trial function,generalized Rayleigh theorem and inequality estimate etc. The estimate is irrelevant to the geometric sense of the domain.

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目的研究广义估计方程的原理与方法 ,探讨参数估计值的具体意义及其在不同类型资料中的应用。方法以某药物治疗慢性浅表性胃炎主症胃脘疼痛的改善为例做对重复测量数据的广义估计方程分析;以该药物治疗萎缩性胃炎主症中胃灼热痛3周与6周疗效为例做对等级资料的广义估计方程分析,并做具体的参数解释。结果 1利用广义估计方程分析结果表明,试验药治疗慢性浅表性胃炎对主症中胃脘疼痛症状的改善优于对照药。2对胃灼热痛疗效的广义估计方程表明,治疗疗程间疗效情况有差异,治疗6周情况改善。但广义估计方程表明试验组与对照组的疗效差异无统计学意义。结论广义估计方程是分析重复测量资料的强有力的手段。对于其参数的解释在实际应用中针对不同的资料有不同的解释方法与角度,从定量与定性角度对偏回归系数进行解释可以为临床药物的研究提供更全面的信息。
Objective To study the principle and methods of generalized estimating equation, and investigate the specific significance of parameter estimation values in the application of different data types. Methods The effi-cacy of a medicine for improving pain in the gastral cavity of chronic superficial gastritis was taken as an example for the generalized estimating equation analysis on repeated measurement data. Meanwhile, the efficacy of the medicine for treating heartburn 3 week and 6 week of atrophic gastritis was taken as an example for the generalized estimating equation analysis on ranked data and specific parameter interpretation. Results ①The results of generalized estimat-ing equation showed that the test drug had better efficacy in improving pain in the gastral cavity of chronic superficial gastritis than that of the control drug. ②The results of generalized estimating equation for the efficacy of treating heartburn showed that there were differences in the treatment c

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对回归模型进行适当变换,得到了线性模型广义最小二乘估计的中偏差及重对数律,并且在均方误差矩阵准则下得到了 Bayes(BE)估计与广义最小二乘估计的2种不同相对效率的上下界.
The moderate deviations and the law of iterated logarithm for the generalized least square estimators in linear models were obtained by transforming the regression model appropriatly. Further, the upper and lower bounds of two kinds of relative efficiency of the Bayes estimator and generalized least squares estimation were obtained in the mean-square error matrix criterion.

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基于广义估计方程和二次推断函数方法，提出了纠偏的广义经验似然方法对纵向数据单指标模型进行统计推断，获得了模型中指标参数分量的极大经验似然估计和纠偏的广义经验对数似然比统计量。证明了相关估计量在一定条件下具有渐近正态性，且纠偏的广义经验对数似然比统计量依分布收敛于χ2分布，利用所得结果，可以构造未知参数的置信域及相关的假设检验。
Based on the generalized estimation equations ( GEE ) and the quadratic inference functions ( QIF ) methods, a bias-corrected generalized empirical likelihood was proposed to make statistical inference for the single-index model with longitudinal data. The maximum empirical likelihood estimator and the bias-corrected generalized empirical log-likelihood ratio statistics for the unknown index parameter in the model were obtained. It is proved that the maximum empirical likelihood estimator is asymptotically normal and the proposed statistics are asymptotically chi-square distributed under certain conditions, and hence they can be applied to construct the confidence region of the index parameter.

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