Empirical Likelihood For Double Generalized Linear Models With Missing Data

With the promotion of total quality management, people are increasingly demanding high quality. From the professional, managerial and statistical quality improvement perspective, has become the focus of everyone’s attention. On statistical terms, in many practical problems, fluctuations affect the quality of the variance may be changing. In order to effectively control the variance, understand the sources of variance, it is necessary to model the variance. Joint mean and variance models and double generalized linear models are important research tools to process heteroscedasticity. With empirical likelihood method, statistical inference is studied in double generalized linear models under missing response. The content contains the following sections:Firstly, the empirical likelihood for joint mean and variance models is proposed. Based on profiled empirical likelihood method, we take joint mean and variance models as the constraints of the profile empirical likelihood ratio function and construct the confidence interval of unknown parameters in joint mean and variance models. Simulation studies and a real example show that this method is useful and effective.Secondly, the empirical likelihood for double generalized linear models is proposed. Based on profiled empirical likelihood method as well, the quasi-likelihood functions of double generalized linear models are considered as the constraints of the profile empirical likelihood ratio function and the confidence intervals of unknown parameters in double generalized linear models are constructed.Finally, simulation studies show that this method is more useful and effective than normal approximation.Finally, a common imputation method in nonparametric statistics-inverse probability weighted method is proposed.The imputed double generalized linear models’ quasi -likelihood functions were considered as the constraints of the profile empirical likelihood ratio function with missing responses.The confidence intervals of unknown parameters in double generalized linear models were constructed. Simulation studies show that, in the double generalized linear models, the inverse probability weighted method and empirical likelihood method are more useful and effective than the unweighted method and normal approximation method respectively.