Statistical Inference Of Heteroscedastic Regression Model With Missing Data

In regression analysis, the general assumption is that the regression model has the homogeneity of variance, but in the real data, there are a lot of data that their variances are heteroscedastic, so we build the variance model based on the heteroscedastic data, it is necessary to understand the influence of variances. In addition, in areas such as medical and financial, the data do not obey the normal distribution strictly, in view of the general joint model, we need to estimate the parameter in these models.On the other hand, how to handle missing data has been a topic of interest to statisticians, missing data may not only result in dispersion of the estimators, will also lead to the distortion of the estimators’variance. The statisticians have been discussing the missing data problems since the1970s. For the lack of research in joint mean and variance models with missing data, this job has both significant theoretical and practical value.This article studies the parametric estimation in three joint models with missing data as follows:First, we propose the parameters estimators for joint mean and variance models of normal distribution with missing data, mainly studied the mean interpolation, regression interpolation and random regression interpolation for missing response at random. Simulation and practice show that random regression interpolation show the effectiveness for the mean parameters estimation and variance parameters estimation compared with the former two methods of interpolation.Second, we investigate the T-type estimation and the least squares estimation in joint mean and variance models when the first and second moments exist, compared the T-estimation and least squares estimation of two estimation methods through simulation studies. We investigate the parameter estimation of the model with missing data. As well as manage the missing data with the maximum cosine distance interpolation and cosine weighting interpolation. Simulation studies show that this model and methods are useful and effective. Especially T-estimate can show more superiority in parameter estimation.Third, in the econometric area and industrial quality improvement experiments, there is a great need to model the mean and dispersion simultaneously. We investigate the estimation of mean parameters and dispersion parameters of double generalized linear models with missing data. As well as manage the missing data with interpolation methods of closest distance and inverse distance weighted. Also, we estimated the unknown parameters using methods of extended quasi-likelihood and pseudo-likelihood. Simulation studies and a real example show that this model and methods are useful and effective.