Estimation Of Error Variances Of Linear Models Based On Ridge Estimation

Empirical likelihood method has attracted the attention of many scholars in the statistical field,It is an important non-parametric statistical method,which is widely used in biological,medical,economic and management fields.Therefore,it is of great value to apply empirical likelihood method to statistical inference of linear models.Least square method plays a fundamental role in parameter estimation of linear models,but when the design matrix X in the case of complex collinearity,the accuracy of least squares estimation becomes lower,the mean square error is larger and the performance is unstable.A biased estimator-ridge estimator can better solve the problem of statistical inference in the case of complex collinearity of design matrix.Therefore,the estimation of linear model error variance under ridge estimation is of great value.In this paper,the empirical likelihood method is used to estimate the error variance of lin-ear models in fixed and random design cases.Under certain regular conditions,the asymptotic normality of the estimator is proved.The asymptotic variance of the estimator is less than the asymptotic variance of the traditional estimator.It can also be seen by numerical simulation that the efficiency of the estimator based on the empirical likelihood method is better than that of the traditional estimator.All right,it further verifies the conclusion of this paper.