Regression via order statistics and their concomitants

Abstract

We consider a five-dimensional normal distribution and derive the exact joint distribution one variable, linear combinations of order statistics from two other variables, and linear combinations of the corresponding concomitants of these order statistics. We show that this joint distribution is a mixture of trivariate unified skew-normal distributions. This mixture representation enables us to predict one variable based on linear combinations of order statistics from two other variables and linear combinations of the corresponding concomitants. We finally illustrate the usefulness of these results by using a real data.

Keywords:

• multivariate unified skew-normal distribution
• order statistics
• mixture distribution
• concomitants of order statistics
• nonlinear prediction

Acknowledgements

This work was done while Ahad Jamalizadeh was visiting the Department of Mathematics and Statistics, McMaster University, Canada, and he is grateful to Prof. Balakrishnan for providing the financial support for this visit.