Research On The Order Of Knockoff Method

Variable selection is an important topic in statistical inference.In 2015,Rina Foygel Barber proposed the Knockoff method.This paper further researches Knockoff’s method and finds that the order of screening variables is different from the order of the absolute values of the true coefficients,and the large coefficient variables cannot be preferentially screened.This paper defines the order of Knockoff and proves that only when the order(1)and(3)are satisfied,as the sample size increases,the error acceptance rate of Knockoff will converge to 0;(2),the probability that the order of the screening variables is consistent with the order of the absolute values of the true coefficients converges to 1.In this paper,Knockoff is improved,using new statistic Z’=Z/s instead of the original statistic Z,and proves that the improved method satisfies the order.This paper calls this Knockoff that satisfies the order as O-Knockoff.Then,in the principal component analysis,the O-Knockoff method is used instead of the variance contribution rate to perform principal component screening,and then PCA-Knockoff is proposed.Finally,the numerical simulation experiment is carried out in this paper.In the experimental results,the order of O-Knockoff compared with Knockoff is more in line with the order of real coefficients.At the same time,in the experimental results,the order of the principal components of the PCA-Knockoff screening is more in line with the order of the actual coefficient size than the order of the variance interpretation rate.