病态方程基于Liu估计的一种迭代估计新方法
发布时间：2018-07-16 15:20
【摘要】：当线性回归模型的设计矩阵病态时,最小二乘(least square,LS)估值方差大且不稳定,已不是一种优良估计。为了减弱病态性,许多有偏估计法如岭估计、主成分估计、Liu估计等被提出。基于Liu估计,引入迭代的思想,提出了一种新的有偏估计法—迭代估计法。借助对称正定矩阵的谱分解,将迭代公式转化为便于解算的解析表达式,并证明迭代公式在修正因子d∈[-1,1]是收敛的。基于Liu估计中修正因子d的确定方法,在均方误差最小的情况下给出最优修正因子d的确定公式。最后,分别利用LS估计、岭估计、Liu估计和提出的迭代估计对两个算例进行计算并给出实验结果。在第一个算例中,对观测向量添加不同的扰动,结果表明迭代估计法具有更强的抗干扰能力;第二个算例的结果表明,迭代估计法所得结果更接近于真值,即迭代估计法在均方误差意义下优于LS估计、岭估计和Liu估计。
[Abstract]:When the design matrix of linear regression model is ill-conditioned, the estimation variance of least square-LS is large and unstable, so it is no longer a good estimate. In order to reduce the morbid property, many biased estimation methods such as Ridge estimation, Principal component estimation and Liu estimation have been proposed. Based on Liu estimation and the idea of iteration, a new biased estimation method-iterative estimation method is proposed. By means of spectral decomposition of symmetric positive definite matrix, the iterative formula is transformed into an analytical expression which is easy to solve, and it is proved that the iterative formula is convergent at the modified factor d 鈭，
本文编号：2126802
[Abstract]:When the design matrix of linear regression model is ill-conditioned, the estimation variance of least square-LS is large and unstable, so it is no longer a good estimate. In order to reduce the morbid property, many biased estimation methods such as Ridge estimation, Principal component estimation and Liu estimation have been proposed. Based on Liu estimation and the idea of iteration, a new biased estimation method-iterative estimation method is proposed. By means of spectral decomposition of symmetric positive definite matrix, the iterative formula is transformed into an analytical expression which is easy to solve, and it is proved that the iterative formula is convergent at the modified factor d 鈭，
本文编号：2126802
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