复共线Gauss-Markov模型参数估计的最小描述长度方法

Parameters Estimation of Multi-Collinearity Gauss-Markov Model Based on Minimum Description Length

Gauss-Markov模型是多元数据分析处理工作中常用的模型,其参数估计与筛选一直是研究的热点。当Gauss-Markov模型的设计矩阵存在复共线性时,常用主成分分析方法来筛选和估计其参数,消去它们之间的复共线性,提高估计准确度。基于最小描述长度原理,提出了一种新的参数筛选估计方法。该方法应用最小描述长度原理选择主成分作为参数,其参数的可靠性较高;从信息的角度看,这种方法的信息损失最小。最后实例说明了该方法的有效性和可靠性。

Gauss-Markov model is frequently used in multivariate data analysis and processing, and its parameter estimation is always a hot issue. Principal component analysis is usually used to select and estimate the parameters when there is multi-collinearity in the coefficient matrix of Gauss-Markov model. Based on information theory and minimum description length (MDL) principle, a novel parameter estimation and selection approach are presented. This new approach, with the help of MDL, selects principal components as the reasonable parameters. The parameters obtained by this way are more reliable, and the information loss can be reduced ,to the minimum from the viewpoint of information theory. In the end, the validity and reliability of the proposed approach are illustrated by an example.