相对误差对相关系数影响的统计特性
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摘要
在两个变量之一有相对误差的情况下,文章研究了相对误差对相关系数的影响。推导了有误差数据的相关系数的总体均数和相对总体均数的近似公式,计算机模拟研究表明,近似公式有较高的精度。从统计特性来看,受相对误差影响,相关系数的绝对值会变小;相对误差越小,相关系数受到的影响也越小;有误差数据的二阶原点矩与二阶中心矩比值越小,相关系数受到的影响也越小。
This paper studies the influence of relative error on correlation coefficient under the condition that one of the two variables has a relative error. The paper also derives an approximate formula for the population mean of the correlation coefficient of error data and the relative population mean. Computer simulation shows that the approximate formula has a relatively higher precision. From the perspective of statistical characteristics, the absolute value of the correlation coefficient decreases under the influence of relative error; the smaller the relative error, the smaller influence the correlation coefficient is affected; the smaller the ratio of second order origin moment to second order center moment of error data, the smaller the influence of correlation coefficient.
This paper studies the influence of relative error on correlation coefficient under the condition that one of the two variables has a relative error. The paper also derives an approximate formula for the population mean of the correlation coefficient of error data and the relative population mean. Computer simulation shows that the approximate formula has a relatively higher precision. From the perspective of statistical characteristics, the absolute value of the correlation coefficient decreases under the influence of relative error; the smaller the relative error, the smaller influence the correlation coefficient is affected; the smaller the ratio of second order origin moment to second order center moment of error data, the smaller the influence of correlation coefficient.
引文
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[7]丁勇.随机误差对线性回归相关系数的影响[J].中国卫生统计,2016,33(6).
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[2]孙振球,徐勇勇.医学统计学(第四版)[M].北京:人民卫生出版社,2014.
[3]刘成友,丁勇.相对误差直线回归模型两种参数估计方法的比较[J].中国卫生统计,2012,29(6).
[4]Charnes A,Cooper W G,Ferguson R O.Optimal Estimation of Executive Compensation by Linear Programming[J].Management Science,1955,(1).
[5]Dielman T E.Least Absolute Value Regression:Recent Contributions[J].Journal of Statistical Computation and Simulation,2005,75(4).
[6]王苗苗,李博峰,沈云中.顾及自变量与因变量误差及相关性的线性回归[J].同济大学学报:自然科学版,2016,44(3).
[7]丁勇.随机误差对线性回归相关系数的影响[J].中国卫生统计,2016,33(6).
[8]叶迎辉,卢光跃.基于相关系数的多天线协作频谱检测[J].电视技术,2016,(4).
[9]林琼芳.环境医学统计学[M].北京:人民卫生出版杜,1989./