基于回归系数检验的多元数据卡方图诊断法  

Multivariate Data's Chi Square Plot Diagnostic Based on Regression Coefficients Testing

作　　者：李长国[1] 索文莉[1] 钟敏[1] 刘艳娜[1] 

机构地区：[1]军事交通学院基础部,天津300161

出　　处：《军事交通学院学报》2014年第10期83-87,共5页Journal of Military Transportation University

基　　金：全军军事学研究生课题(2012JY002-418)

摘　　要：在多元正态数据的卡方图诊断中,针对简单线性回归模型检验法的限制,提出基于统计模拟的系数检验法。首先通过加权最小二乘法得到回归系数的估计量,再使用蒙特卡洛模拟方法得到2个估计量的经验分布,进而得到2个估计量的经验容许区间,以此作为检验回归系数显著性的置信区间,最后得到不同样本容量、不同样本维数情况下的检验临界值。结合3个真实案例,给出不同检验方法的检验功效,结果表明回归系数检验法不但弥补了图像诊断主观随意性的不足,也具有较高的检验功效。In the chi - square plot diagnosis of multivariate normal data, aiming at the limitations of simple linear regression model testing method, the statistical simulation - based coefficients testing method is proposed. First, the estimates of re- gression coefficients are obtained via weighted least squares, and then the empirical distribution of 2 estimates is obtained by using Monte Carlo simulation. Then the empirical tolerance intervals of the 2 estimates are obtained as the confidence in- tervals for testing the significance of regression coefficients. Finally, the cut - off values under the situation of different samples and different dimensions are obtained. Combining with 3 real cases, the test power of different testing methods are given. It concludes that the regression coefficient testing method not only covers the shortage of imaging diagnosis＇ subjec- tive arbitrariness, but also has stronger test power.

关 键 词：多元正态分布 卡方图 加权最小二乘 庞弗洛尼检验 蒙特卡洛 经验容许区间 

分 类 号：O212.4[理学—概率论与数理统计]