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- 2017
病态方程基于Liu估计的一种迭代估计新方法
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Abstract:
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
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