Using (ECM) Algorithm to Estimate the Missing Values and Make Comparison between (MLE) and (GA) Algorithm for Estimating Parameters of Multivariate Skew Normal Distribution (MSN)

Abstract

The estimation of statistical parameters for multivariate data leads to waste in the information if the missing values are neglected, which will subsequently lead to inaccurate estimates. Therefore, the incomplete data must be estimated using one of the statistical estimation methods to obtain accurate results and thus obtaining good estimates for the parameters.The aim of this paper is to estimate the missing values for the multivariate skew normal distribution function using the Expectation Conditional Maximization (ECM) algorithm. After estimating the missing values, the parameters are estimated using Maximum Likelihood Estimation (MLE) with the Newton-Raphson algorithm, as well as using the Genetic Algorithm (GA). Using simulation, the Mean Squared Error (MSE) was calculated to find out which method is the best for estimation by comparing the two methods using different sample sizes (400, 600, and 800). The (GA) that is based on the (ECM) algorithm to estimate the missing values proved to be better and more efficient than the (MLE) method in terms of the results.