度量误差对模型参数估计值的影响及参数估计方法的比较研究

Study on Impact of Measurement Error on Model and Compare of Parameter Estimate Methods

基于模型V=aDb,首先在Matlab下用模拟实验的方法,研究了度量误差对模型参数估计的影响,结果表明:当V的误差固定而D的误差不断增大时,用通常最小二乘法对模型进行参数估计,参数a的估计值不断增大,参数b的估计值不断减小,参数估计值随着 D的度量误差的增大越来越远离参数真实值;然后对消除度量误差影响的参数估计方法进行研究,分别用回归校准法、模拟外推法和度量误差模型方法对V和D都有度量误差的数据进行参数估计,结果表明:回归校准法、模拟外推法和度量误差模型方法都能得到参数的无偏估计,克服了用通常最小二乘法进行估计造成的参数估计的系统偏差,结果进一步表明度量误差模型方法优于回归校准法和模拟外推法．

Based on the model V = aD^b, by means of simulation method, the impact of measurement error on the model is firstly studied. The result indicates that： with the fixed error of V, parameter a has the trend of becoming bigger, parameter b becoming smaller while the error of D becoming bigger. The estimated value of parameter is getting away from its real value. Then Simulation Extrapolation, Regression Calibration and Measurement Error Model are used to estimate the model parameters. All the estimates of the three methods are unbias and the Measurement Error Model is the best.