Statistical Inference Of Location And Mean Regression Model Under Skew Laplace Normal Data

The normal distribution is the most commonly used distribution in statistical analysis.In the traditional statistical research,it is usually assumed that the data have symmetry.But in fields such as medicine,finance and social economy,there is a wealth of skewed data.In order to study this kind of problem,statisticians put forward many statistical models with asymmetry,among which the common ones are those based on skew normal distribution and skew-t distribution.However,there are also a large number of skewed and thick-tailed data in real life and application.At this time,the methods or models under normal distribution,skew normal distribution and skew-t distribution are no longer applicable to such data.Therefore,it is necessary to establish a statistical model under skew Laplace normal distribution.In addition,the importance of location and mean regression model in skew Laplace normal distribution is considered.Based on skew Laplace normal data,this paper studies the maximum likelihood estimation,ridge estimation of location and mean regression models and statistical diagnosis of location regression model.The research contents are summarized as follows:(1)Establish location and mean regression models for skew Laplace normal data.Based on EM algorithm,the maximum likelihood estimation of location and mean regression model is studied,and the specific algorithm steps are given.Finally,through the simulation analysis and the use of film box office data for example analysis,so as to illustrate the scientific nature and rationality of the research model and method.(2)On the basis of the content of the first part,considering that when the explanatory variables in the data have multicollinearity,it will have a negative impact on the maximum likelihood estimation,and ridge estimation is a common method to solve this problem.So EM algorithm is used to estimate the ridge of location and mean regression model,and the validity and practicability of the model and method were demonstrated through simulation analysis and the example analysis of wine data from Vinho wine,a unique product from Minio region of Portugal.(3)Pena distance is extended from linear regression model under skew normal distribution to linear regression model under skew Laplace normal distribution,so that it can not only diagnose skew normal data,but also can diagnose skew Laplace normal data.Therefore,the statistical diagnosis of location regression model under skew Laplace normal data is studied.The EM algorithm is used to compare the likelihood distance,Cook distance and Pena distance.The model and method are proved to be scientific through simulation research and BOQ equipment data analysis.