Linear Regression Model With Random Constraints And Bayes Methods Of Statistical Diagnostics

In this paper, we discuss the linear regression model with the random constraints,give the general LS estimation, introduce its residuals, and show that the CDM is equiva-lent to the mean shift outlier model(MSOM) for diagnostics purpose, then we investigatethe common statistics: Cook distance, W-K statistic, Covariance Ratio, Likelihood dis-tance and so on. We discuss the heteroscedastictiy and obtain the score statistic aboutthe model, an example is given to illustrate our results. After that, we introduce theBayesian method of the linear regression model, use the Bayesian theories to estimatethe coefficient parameter, have educed Parametric Empirical Bayes (PEB) estimation ofparameter that is different from what Zhang et al.[47] described, and study its supe-riorities over the ordinary least squares (LS) estimations, then investigate the commoncase deletion rnodel(CDM), and its statistics; an example is given to illustrate our results,provide the diagram.