Characteristic Test For Error Distribution In Multivariate Linear Model

The test of error distribution in multivariate linear model has been a hot research topic in the field of statistics.The estimation and test of multivariate linear model is based on the theory of statistical inference under the hypothesis that the error is subject to certain distribution.If the error distribution is judged to be incorrect,a series of statistical inferences based on the error will lose significance.So it is very important to test the error distribution in multivariate linear model.The basic hypothesis of the error distribution in the classical multivariate linear model is the multivariate normal distribution.In the generalized multivariate analysis,the error distribution of the multivariate linear model is extended to the elliptical symmetry distribution.In the existing literature about multivariate linear model of the error distribution,the testing for normality and elliptical symmetry of errors in multivariate linear model and how to propose a suitable model to better fit the actual data to predict and reflect the various features of the actual data of the research area is not deep enough,the power of test statistic is not high problems.Therefore,it is necessary to further study the test of error distribution in multivariate linear model,and it is very important to propose a more efficient and simple method of error distribution test.In this paper,we introduce the basic theory of characteristic test of spherical uniform distribution.The characteristic test statistic for a certain correction is applied to the test for error distribution in multivariate linear model.We studied error distributions of multivariate normal and elliptical symmetric test in multivariate linear model.The main conclusions are as follows:(1)Multivariate normality characteristic test for error distribution in multivariate linear model is proposed.The algorithm steps of the characteristic test statistic of the error distribution and the simulation critical values are given.The characteristic test statistic for error distribution has carried on power simulation.(2)Elliptical symmetric characteristic test for error distribution in multivariate linear model is proposed.The algorithm steps of the characteristic test statistic of the error distribution and the simulation critical values are given.The characteristic test statistic for error distribution has carried on power simulation.(3)Using the relationship between the physical indexes of cotton and yarn quality index,we set up a multivariate linear regression model.Applying the characteristic test statistics for error distribution,the new multivariate linear regression model has carried on normality test.Meanwhile,combining with the actual spinning data,we use correction model to get the prediction of out-of-sample and predict ellipsoid.