Statistical Inference Of Heteroscedasticity Modal Based On Missing Skewness Data

Statisticians have always been investigated kinds of data, in which exists skew data with heavier tail. It appears mostly in areas such as finance, economics, biomedical and environmental science and have unique characteristics and functions. While in practice, we encounter some heteroscedastic data, which break the assumption of the homoscedasticity of observed data. Meanwhile, in many practical applications, it’s very useful to model the variance to identify the source of variability and interest in its own right in control process. Since the 1970s, more and more people have focused on the problems of missing data. Not only the effect of the estimation of parameters, but the distortion of variances cause the usual means useless. As a result, large of methods have been post to solve missing date. As far as we can seen, little work have been done about missing skew data, especially the joint models with missing skew data.In this paper, based on missing skew data, we studies the statistical inference problems of a joint location, scale model and a joint location, scale and skewness model. The main content includes the following sections:Firstly, we investigate the joint location and scale models with missing skew-normal data and regression imputation, random regression imputation methods in the case of missing response. Meanwhile, we propose a new random regression imputation method named corrected stochastic regression imputation based on the characteristics of the distribution. Compared with regression imputation, random regression imputation methods, simulation studies and a real example show the corrected random regression imputation method is useful and effective to revise the skewness parameter in joint models.Secondly, we study the EM-type algorithms based on the joint location, scale and skewness models with missing skew-normal data. The applications in complete skew data and missing skew data are given in detail. Simulation studies show the EM-type algorithms is useful and effective.Thirdly, we consider the problem of joint location and scale models with missing skew-t-normal distribution. The EM algorithm is used in the complete data’s parameters estimation. The regression imputation and random regression imputation are studied in case of missing response at random. Stimulation shows that the random regression imputation deal with variance parameters estimation effectively compared with the regression imputation.