Statistical Inference Of High Dimensional Seemingly Unrelated Regression Model

Equations in seemingly unrelated regression model are correlated to each oth-er through the disturbances,although by construction they are seemingly unrelated Hence,methods which exploit the correlation between equations can increase the accu-racy in estimation.With the advent of the era of big data,more and more information are serially independent but contemporaneously correlated.Seemingly unrelated re-gression model can describe this correlation properly.This paper focuses on statistical inference for high dimensional seemingly unrelated regression model.We give two im-proved estimator,and propose a new method for test the contemporaneous correlation of disturbances in high dimensional seemingly unrelated regression models.Following are the main resultsWe prove that in a high-dimensional seemingly unrelated regression model,the maximum likelihood estimator does not exist.and the covariance of Zellner's estimator tends to infinity with the number of equations going to infinity.As an alternative,a new improved estimator based on the conditional expectation is proposed.It is proved that under some condition the new improved estimator is equivalent to generalized least squares estimator.Inspired by Zellner's two-stage estimator,the two-stage improved estimator is defined.And from the analysis of covariance matrix only the equations which are highly correlated with the first equation are used to improve the estimator Thus an improved Zellner's estimator based on the highly correlated equations is pro-posed.And the highly correlation is determined by hypothesis testings.Simulations show that the proposed estimator outperforms the ordinary least squares estimator and Zellner's estimatorGeneralized canonical correlation variable pairs are defined firstly.Based on the definitions,a new estimator of regression coefficients in SUR models is proposed,and its properties are also discussed.Simulations show that the proposed estimator outper-forms the ordinary least squares estimatorThe problem of testing the contemporaneous correlation of disturbances in high dimensional seemingly unrelated regression models have been discussed.Based on the maximum value of sample correlation coefficients,a new test statistic is proposed.And the asymptotically distributed of it is derived.The results of simulations show that the proposed test statistic is superior to others in the case that the seemingly unrelated regression models have low global correlation but high local correlation.