【摘要】：當(dāng)線性回歸模型的設(shè)計矩陣病態(tài)時,最小二乘(least square,LS)估值方差大且不穩(wěn)定,已不是一種優(yōu)良估計。為了減弱病態(tài)性,許多有偏估計法如嶺估計、主成分估計、Liu估計等被提出�；贚iu估計,引入迭代的思想,提出了一種新的有偏估計法—迭代估計法。借助對稱正定矩陣的譜分解,將迭代公式轉(zhuǎn)化為便于解算的解析表達式,并證明迭代公式在修正因子d∈[-1,1]是收斂的�；贚iu估計中修正因子d的確定方法,在均方誤差最小的情況下給出最優(yōu)修正因子d的確定公式。最后,分別利用LS估計、嶺估計、Liu估計和提出的迭代估計對兩個算例進行計算并給出實驗結(jié)果。在第一個算例中,對觀測向量添加不同的擾動,結(jié)果表明迭代估計法具有更強的抗干擾能力;第二個算例的結(jié)果表明,迭代估計法所得結(jié)果更接近于真值,即迭代估計法在均方誤差意義下優(yōu)于LS估計、嶺估計和Liu估計。
[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，

本文編號：2126802