摘要
经典的一元和多元线性回归模型多采用最小二乘方法进行参数解算,但最小二乘估计无抗差能力,遇到异常值干扰易导致参数估值出现偏差。为提高回归分析方法的抗差性,将中位数引入回归分析方法中,提出了一种基于中位数的回归分析方法。详细分析了回归分析的相关理论以及基于中位数的回归分析方法的基本原理;以淮北某矿区建筑物的实际变形监测数据为例,分别对变形监测数据进行了最小二乘回归分析、抗差最小二乘回归分析以及中位数回归分析,并对其拟合及预测效果进行了对比。结果表明:观测量受到粗差污染时,中位数回归分析方法可有效抵抗异常值的影响,拟合效果及预计结果均优于其他2种方法,对于提高矿区变形监测数据的处理精度及效率有一定的参考价值。
Most of the parameters of the classical one and multiple variates linear regression models are calculated by adopting the least square estimation method,however,the least square estimation method without the anti-error ability,the performance of the least squares estimation method will be degraded by outliers,thus,the deviation is appeared.In order to improve the anti-error ability of the regression analysis method,the median is introduced to regression analysis method,a new regression analysis method based on median is proposed.The correlative theories of regression method and its application in deformation monitoring data processing are discussed and the basic principle of the median regression analysis method proposed in this paper is also analyzed in detail.The actual deformation monitoring data of the buildings of a mining area in Huaibei city are analyzed by the least squares regression analyssi method,the least squares estimation regression analysis method based on anti-error and the median regression analysis method respectively.The experimental results show that when the observed values is polluted by gross errors,the influence of outliers can be resisted effectively by the median regression analysis method,the fitting effect and prediction results of the median regression analysis method is superior to the other methods,therefore,it has some reference for improving the processing precision and efficiency of the deformation monitoring data in mining area.
出处
《金属矿山》
CAS
北大核心
2016年第5期192-195,共4页
Metal Mine
基金
国家自然科学基金项目(编号:41504032)
江苏省自然科学基金项目(编号:BK20150175)
江苏高校优势学科建设工程项目(编号:PAPD SA1102)
关键词
变形监测
中位数
回归分析
数据处理
最小二乘估计
Deformation monitoring
Median
Regression analysis
Data processing
Least square estimation
