Comparison of Covariance Matrices of Predictors in Seemingly Unrelated Regression Models


Güler N., Eriş Büyükkaya M., Yiğit M.

Indian Journal of Pure and Applied Mathematics, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1007/s13226-021-00174-w
  • Journal Name: Indian Journal of Pure and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded, Scopus, INSPEC, zbMATH
  • Keywords: BLUP, Covariance matrix, Inertia, OLSP, Rank, Seemingly unrelated regression model, LINEAR UNBIASED PREDICTION, EQUALITIES, ESTIMATORS

Abstract

© 2021, The Indian National Science Academy.This paper considers comparison problems of predictor and estimator in the context of seemingly unrelated regression models (SURM s). SURM s are a class of multiple regression equations with correlated errors among the equations from linear regression models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUP s) and the ordinary least squares predictors (OLSP s) of unknown vectors under SURM s by using various rank and inertia formulas of block matrices. The results for comparisons of the best linear unbiased estimators (BLUE s) and the ordinary least squares estimators (OLSE s) in the models are also considered.