| 用蒙特卡洛模拟法计算正交最小二乘法拟合参数的标准偏差 |
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| 引用本文： | 李玉武,刘咸德.用蒙特卡洛模拟法计算正交最小二乘法拟合参数的标准偏差[J].岩矿测试,2002,21(1):24-28. |
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| 作者姓名： | 李玉武 刘咸德 |
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| 作者单位： | 国家环境分析测试中心,北京,100029 |
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| 基金项目： | 教育部留学回国人员科研启动基金 (6 79/ 1998)，国家自然科学基金 (2 97770 2 9)，中国 -比利时双边科学技术合作项目 (BWTS 97/ 71) |
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| 摘 要： | 介绍了一种计算正交最小二乘法拟合参数标准偏差的新方法－蒙特卡洛模拟法，并以电子探针微区分析技术分析环境样品的数据为例，对用于计算经典最小二乘法回归系数标准偏差的公式法和蒙特卡洛模拟法进行了比较。计算结果表明，两者完全相符，蒙特卡洛模拟法的计算结果正确、可靠。考察了模拟次数对计算结果的影响。模拟次数大于500时，计算结果趋于稳定，计算所需时间在1min以内。拟合方差与回归系数标准偏差存在明显的相关关系。线性模型能解释的方差越大，回归系数标准偏差越小。蒙特卡洛模拟法特别适合于非线性模型拟合参数标准偏差的计算。
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| 关 键 词： | 蒙特卡洛模拟法 正交最小二乘法 回归系数 标准偏差 电子探针 环境样品 |
| 文章编号： | 0254-5357(2002)01-0024-05 |
| 修稿时间： | 2001年3月23日 |
Estimating Standard Deviation of Regression Coefficient in Orthogonal Least Squares by Monte Carlo Simulation |
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| LI Yu wu,LIU Xian de.Estimating Standard Deviation of Regression Coefficient in Orthogonal Least Squares by Monte Carlo Simulation[J].Rock and Mineral Analysis,2002,21(1):24-28. |
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| Authors: | LI Yu wu LIU Xian de |
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| Abstract: | A new method, Monte Carlo simulation, to estimate standard deviation of regression coefficients in orthogonal least squares is presented in this paper. The results by formula or by Monte Carlo simulation used in classical least squares are compared based on electron probe microanalysis data sets which are used to estimate the ratio of K to Cl and S X ray intensity for determining the elemental speciation. It is validated that standard deviation of regression coefficient by Monte Carlo simulation is in line with that of formula. The effect of the number of simulation on results is investigated. The result tends to a stable value after more than 500 repetitions. It is found that the more the variance explained by the linear model, the smaller the standard deviation of regression coefficient. Monte Carlo simulation is specially suited to non linear or complex mathematical models. |
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| Keywords: | Monte Carlo simulation orthogonal least squares standard deviation of regression coefficients |
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