@Article{JICS-13-269,
author = {Qingli Pan and Chuanlin Zhang},
title = {Confidence ellipsoids for the primary regression coefficients in m- equation seemingly unrelated regression models},
journal = {Journal of Information and Computing Science},
year = {2018},
volume = {13},
number = {4},
pages = {269--282},
abstract = { For  a  m-equation  seemingly  unrelated  regression(SUR)  model,  this  paper  derives  two  basic 
confidence  ellipsoids(CEs)  respectively  based  on  the  two-stage  estimation  and  maximum  likelihood 
estimation(MLE), and corrects the two CEs using the Bartlett correction method, resulting in four new CEs. 
In  the  meantime  via  using  the  partition  matrix,  we  derive  a  new  matrix-derivative-based  formulation  of 
Fisher's information matrix for calculating the maximum likelihood estimator of the m-equation SUR model. 
By  Monte  Carlo  simulation,  the  coverage  probabilities  and  average  volumetric  characteristics  of  CEs  are 
compared under different sample values and different correlation coefficients. Moreover, it is proved that the 
CE based on the second bartlett correction method performs better even in the case of small samples. Finally, 
we apply these CEs to the actual data for analysis. The CEs of the SUR model with multiple equations are 
found to be more accurate than the case with only two equations. 
},
issn = {3080-180X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22436.html}
}