Multiple Linear Regression Model With Linear Constraints, Statistical Diagnostics

Multivariate regression analysis is one of mathematical statistics methods to deal with interdependent relationships among a number of variables. The interdependent relationships exist in many practical problems. Along with the popularization of computer and the produce of kinds of statistical analysis software, the multivariate regression model has also received more and more attention. In some practical problems, regression coefficients of this model are not arbitrary value, possibly they have certain restraint. So it is very necessary to research the restricted multivariate regression model.In this paper, we mainly discuss some preliminary studies about statistical diagnostics for one kind of restricted multivariate linear regression model. At first, we give the parameters estimation of this model. After that, the problem of outlier test is considered by giving the equivalence relations of estimators and statistics in multivariate case deletion model and mean shift outlier model under the restricted condition. Then, we get some test statistics through influence analysis for this model, for example cook statistic and welsch-kuh statistic and so on. In addition, an example is given to illustrate our results.