Local Influence For Some Statistical Models

Statisticians have paid extensively continuous attention to statistic diagnostics sinceits development, whose main task is to exam the reasonability of the postulated modelwith known dataset, and is a main step in data analysis. The test of influential point, as asupplement to the residual analysis, is a hot issue in statistic diagnostics, and has beenbroadly applied shortly after its proposal. This thesis mainly contributes to localinfluential analysis and related problems for several statistic models whenmulti-collinearity presents in independent variables.In linear modes, we firstly discuss the sufficient and necessary conditions when theresidues for the unified biased estimates and almost unbiased unified biased estimates isbetter than that of the least square estimates under mean square error matrix. Secondly,we discuss the local influential analysis for the two-parameter estimates, and obtain thegeneralized influential function and Cook statistic for variance perturbation,independent variable perturbation and response perturbation. Finally, we discuss thelocal influential analysis for the ridge estimator of linear model under stochasticrestrictions, we obtain the MLE by using the augmented model, and then generalize twokinds of the local influential analysis based on likelihood functions to biased estimatorunder stochastic restrictions, obtain the diagnostic statistic under three types ofperturbations. We also give some numerical examples to illustrate our results.In elliptical linear models, we study the local influential analysis under equalityconstraints. We firstly obtain the estimates using the penalized likelihood function anditeration methods, and then obtain the diagnostic statistic under three types ofperturbations by generalizing the local influential analysis based on likelihood functions.Numerical examples are also given to illustrate our results.For generalized linear models (GLM), we study the local influential analysis underridge estimates. We firstly introduce the GLM and its ridge estimates, then by definingthe likelihood function, generalize the local influential analysis to the biased estimatesof this model, obtaining the diagnostic statistic under four types of perturbations.Numerical examples are also given to illustrate our results.For generalized linear symmetric models (GLSM), we study the local influentialanalysis under equality constraints. We use iteration to obtain the estimates, and obtainthe diagnostic statistic under four types of perturbations based on the penalized likelihood functions.