Estimation And Test Of Parameter In The Multiple Multivariate Lineal Model With General Linear Constraint

About testing the hypothesis PПQ=0in the multiple multivariate lineal model Yn×q=Xn×pПp×q+ε, there exist several methods which are introduced in the references listed in the last chapter and the testing statistics are given. While with regard to the parameter estimation under the null hypothesis, no papers and documents were found to study it. When introducing the vector auto-regression, the author didn’t give the explicit parameter expression with the model given the similar constraint RП=0, instead, only iteration method was applied to approximate the true value. Though we can test the hypothesis regardless what the parameter estimation is, when the hypothesis holds, that is to say, the problem can’t be skipped with the parameter indeed satisfying the constraints condition. Without given the explicit expression of the parameter, no any further studying can be continued. Applying derivation with respect to the matrix and some skillful transform, this paper gives the solution of the parameter estimation which the most important work of the paper and study about its distribution as well as its confident interval. In the last part, the paper proves that a lot of problem of the parameter testing in the multivariate analysis, including variable selection in the multiple multivariate linear model, expectation test among several multivariate normal populations, additional information test, and the profile analysis between several groups followed normal multivariate distribution, etc, is just some special cases of this paper’s conclusion which means that the achievements of the paper has wide applications.