【摘要】 经典最小二乘回归模型假设自变量没有误差而所有误差都集中于响应变量,但是许多应用领域中实际问题的自变量含有噪声数据,往往不符合这个假设,经典最小二乘回归模型不再适用。为克服这一缺陷,介绍了正交最小二乘回归模型和参数估计算法。对经典最小二乘和正交最小二乘回归系数进行了理论分析和计算机数值仿真,结果表明当自变量和响应变量都含有误差时,正交最小二乘法优于经典最小二乘法。最后将经典最小二乘法和正交最小二乘法用于蒙城地震台2001~2006年地震数据,确定了台站震级偏差校正公式,并对它们的结果进行了详细比较。更多还原

【Abstract】 The classical least square regression model assume that the independent variables are measured exactly and all the errors are focused on the response variables.However,in many real problems in certain areas,some of the independent variables are contaminated with errors;the classical least square regression model can’t deal with this problem.To overcome this drawback,the orthogonal least square regression model is introduced.The comparisons between orthogonal least square regression and classical least square regression are done through theory analysis and computer simulation.Our results validate that when independent and independent variables are corrupted by noise,the estimation obtained with the orthogonal least square regression are superior to those with the classical least square regression.At last,the orthogonal least square regression is employed to earthquake catalogues of Mengcheng seismic station from 2001 to 2006,the results obtained by the above two methods are compared in detail.更多还原