Statistical Diagnostics For Quasi-likelihood Nonlinear Models

The quasi-likelihood nonlinear model has universal applicability because it only needs the first and second moments of known response variables Y and does not need the specific distribution of Y.In view of this,this paper makes a systematic statistical diagnosis and analysis of quasi-likelihood nonlinear model by empirical likelihood method.First of all,this paper studies the parameter estimation of quasi-likelihood nonlinear model.Firstly,the estimation equation of the quasi-likelihood nonlinear model is obtained from the quasi-score function,and then the empirical likelihood method is applied to the model to obtain the empirical logarithmic likelihood ratio function,and then get the empirical likelihood estimation of parameters.Secondly,we study the case deletion modeland the local influence analysis of quasi-likelihood nonlinear model and obtain the diagnostical statistic.For the case deletion model,we derive the estimatiion of ? after deleting the i-th data point and derive the first-order approximation formula of ?(i).The difference between ? and ?(i)is then measured by defining the empirical likelihood distance and the empirical Cook distance.For the local influence analysis of the quasi-likelihood nonlinear model,the research is mainly affected by the perturbation.Firstly,we obtain the empirical likelihood distance of the model after perturbation and the second-order approximation formula.Then influence curvature based on empirical likelihood of the quasi-likelihood nonlinear model is studied in detail.Finally,on the basis of theoretical analysis,an example of quasi-likelihood nonlinear model is analyzed with R language.To verify the effectiveness and rationality of the above statistical methods,we obtain the empirical likelihood estimation of quasi-likelihood nonlinear model.Outliers and strong influence points were obtained by standard residuals and empirical Cook distance.