Using some methods to estimate the parameters of the Multivariate Skew Normal (MSN) distribution function with missing data

Nayef Al-Qazaz, Qutaiba Nabeel; Shawkat, Lina Nidhal

doi:10.22075/ijnaa.2021.5932

Using some methods to estimate the parameters of the Multivariate Skew Normal (MSN) distribution function with missing data

Document Type : Research Paper

Authors

Qutaiba Nabeel Nayef Al-Qazaz

Lina Nidhal Shawkat

University of Baghdad ,College of Administration & Economics, Statistics Department, Iraq

10.22075/ijnaa.2021.5932

Abstract

The estimation of statistical parameters for multivariate data can lead to wasted information if the missing values are neglected, which in return will 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.
Missing values is considered one of the most important problems that researchers encounter and the most common, and in the case of the multivariate skew normal distribution (MSN) the presence of this problem will lead to weak and misleading conclusions for the research, which calls for treating this problem and in return obtaining efficient and convincing results. The aim of this paper is to estimate the missing values for the multivariate skew normal distribution function using the K-nearest neighbors Imputation (KNN). After estimating the missing values, the parameters are estimated using Genetic Algorithm (GA), and the Bayesian Approach was also used to estimate the missing values and find the estimates for the parameters. 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 (KNN) algorithm to estimate the missing values proved to be better and more efficient than the Bayesian Approach in terms of the results.

Keywords

Multivariate Skew Normal distribution (MSN)

K-Nearest Neighbors Imputation (KNN)

Genetic Algorithm (GA)

Bayesian Approach

Mean Squared Error (MSE)

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