有约束多元回归分析中的C_p统计量

In this paper, Mallow's C_p statistic in multiple linear regression analysis is genera-lized to the case with linear equality constrained conditions.The C_(p,m_1) statistic is introduced asC_(p,m_1)=RS_p~2/σ~2-m 2(p-m_1),where m and m_1 are respectively the numbers of the observed data of the variables andof the constrained conditions, p>m_1 is the number of the remaining regression variablesafter q variables are rejected from the n regression variables (p q=n) RS_p~2 is the sumof squares of residuals of the regression for the p remaining variables, σ~2 is an unbiasedestimate of variance σ~2. The properties of the C_(p,m_1) statistic and a method for selectingand analyzing variables in constrained multiple linear regression analysis by using theC_(p,m_1) statistic are discussed in detail.