Nonparametric Theil-Sen Method For Linear Mixed Model

The Theil-Sen estimation is Theil[3]proposed in 1950,and Sen[17]was popularized in 1968.The basic estimation idea of this method is that in the linear regression model,the slope of the two pairs of observations is solved first and the median of the slope is used as the estimated value of the slope parameter.In this paper,we consider the linear mixed model,apply Theil-Sen to the estimation of regression parameters in fixed effects,and prove the consistency of estimators.In the previous literature,it is assumed that the random and random error of the individual satisfies the normal distribution,and the maximum likelihood estimation is used to obtain the best linear unbiased estimation of the fixed effect and the random effect.However,the estimation depends on the covariance structure of the fixed and random effects.So there are a lot of discussions on covariance in the literature,and the cyclic iterative algorithm is often used.To the numerical solution.Under the assumption of the general random error and random effect distribution,firstly,the Theil-Sen estimation is used to estimate the fixed effect parameters,then the variance of the random effect and the random error is estimated.The cyclic iterative algorithm is avoided,the calculation is more simple,the applicability of the linear mixed model is more extensive,and the Theil-Sen estimation is robust.We compare the maxi-mum likelihood estimation and Theil-Sen estimation by random simulation.The results of random simulation show that when both the random effect and the random error satisfy the normal distribution,the Theil-Sen estimation is similar to the maximum likelihood estimation.When there is an abnormal value,the estimation of the parameter and the random effect variance of the fixed effect is better than the likelihood estimation when there is an abnormal value;in the general random effect and random effect,the Theil-Sen is better than the likelihood estimation.