Heteroscedasticity Model Based On Lognormal Distribution Of Statistical Inference

Log-normal distribution heteroscedastic regression model is natural extension and development of normally distributed heteroscedastic regression model. Because many practical problems in the analysis, most of the collected data are not strictly obey the normal distribution, but in order to obtain timely, accurate information, we need to transform these data. Box-Cox transformation is one of the most famous data transformations, and logarithmic transformation of the Box-Cox transformation is the most important and one of the most commonly used transformations due to logarithmic transform the fine nature of the log-normal distribution model is widely used, particularly in the financial and economic fields, reliability and life testing of the application. On the other hand, a lot of literature proposed modeling the mean is very effective and flexible. However, in many applications, especially in the economic field and to improve the quality of industrial products test, there are a lot of heteroscedastic data, it is necessary to model the variance in order to better understand the sources of variance, to effective control of the variance. Thus, modeling of variance can be as important as that of the mean. Compared to modeling the mean, modeling the variance studies at the initial stage.In this article, using the maximum likelihood estimation method, we systematically investigated statistical inference about the log-normal distribution heteroscedastic regression model, mainly including the following three parts.Firstly, we investigate the maximum likelihood estimation of joint log-mean and log-variance model. The consistency and asymptotic normality of the estimators are proved. Simulation studies and two examples show that these results and methods are simple and effective.Secondly, we consider the maximum likelihood estimation of joint mean and dispersion generalized linear model. The consistency and asymptotic normality of the estimators are established. Simulation studies and two examples show that these results and methods are useful and effective.Thirdly, we investigate the maximum likelihood estimation of joint mean and variance model based on Box-Cox transformation. We firstly consider maximum profile likelihood estimator of Box-Cox transformation parameter. Then we investigate the maximum likelihood estimation of joint mean and variance model. Simulation studies and a real example show that these results and methods are useful and effective.