Parameter estimates for mean and mode regression models with skew-normal errors
The classic multivariate linear regression model requires the residuals to meet the Gauss-Markov Conditions(G-M),which is often difficult to meet in real life due to the randomness of the data.Using the skew-normal distribution proposed by Sahu in 2003 to expand the classical regression model,the approximate expression of the mode is given under the skew-normal distribution,and the multivariate linear regression models of the mean and mode are established under the skew-normal distribution.In order to estimate the unknown parameters of the model,the EM algorithm is constructed by using the hierarchical representation of the skew-normal distribution.The two-point step gradient descent algorithm is uniformly given in M step,and the explicit iteration expression is also given for the mean regression model.Finally,the feasibility of the two regression models is discussed through simulation studies and examples analysis.
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