Confidence ellipsoids for the primary regression coefficients in m- equation seemingly unrelated regression models
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@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 = {2024},
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 = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22436.html}
}
TY - JOUR
T1 - Confidence ellipsoids for the primary regression coefficients in m- equation seemingly unrelated regression models
AU - Qingli Pan and Chuanlin Zhang
JO - Journal of Information and Computing Science
VL - 4
SP - 269
EP - 282
PY - 2024
DA - 2024/01
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22436.html
KW - Keywords:Seemingly unrelated regression, Confidence ellipsoids, Bartlett correction, Maximum
likelihood estimation.
AB - 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.
Qingli Pan and Chuanlin Zhang. (2024). Confidence ellipsoids for the primary regression coefficients in m- equation seemingly unrelated regression models.
Journal of Information and Computing Science. 13 (4).
269-282.
doi:
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