Statistical Inference Based On Second-Order Least Squares Estimation

Least squares estimation plays a very important role in the theory and application of mathematics,statistics,medicine,engineering,and more disciplines.More and more research areas use the least squares estimation to do study.Many experts and scholars have also done a lot of research in detail on this method,and they put forward many methods to improve the least squares estimation.This paper mainly introduces a new parameter estimation method-second-order least squares estimation,and employ it to make statistical inference for the regression parameters.The second-order least squares estimation(SLS)method is extended on the basis of the ordinary least squares estimation(OLS)method by using high order data information The main idea of the second-order least squares estimation is to minimize the square of the difference of the dependent variable's square and its second-order conditional moment and the square of the difference of the dependent variable and its first-order conditional moment.It increases the variance estimation of the error variable.This paper studies interval estimation and hypothesis testing of linear regression models with asymmetric distribution error variables.Three conclusions are summed up in this paper.Firstly,with the sample number decreasing,the mean squared errors of regression parameters from the second-order least squares estimation are smaller than those via the ordinary least squares estimation Secondly,the interval estimation of regression parameters from the second-order least squares estimation is shorter than thoes via the ordinary least squares estimation under the same confidence level.Thirdly,for any parameters from the alternative hypothesis,the frequencies of rejecting null hypothesis from the second-order least squares estimation are higher than those via the ordinary least squares estimation.In addition,when the random error distribution is unknown,we can also use the second-order least squares estimation method to do statistical inference for regression parameters.