scholarly journals Capturing a Change in the Covariance Structure of a Multivariate Process

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 156
Author(s):  
Andriette Bekker ◽  
Johannes T. Ferreira ◽  
Schalk W. Human ◽  
Karien Adamski
Keyword(s):  
Covariance Matrix ◽  
Random Variables ◽  
Covariance Structure ◽  
Multivariate Normal ◽  
New Approach ◽  
Downward Shift ◽  
Consecutive Time ◽  
Time Periods ◽  
Unknown Covariance ◽  
Mean Vector

This research is inspired from monitoring the process covariance structure of q attributes where samples are independent, having been collected from a multivariate normal distribution with known mean vector and unknown covariance matrix. The focus is on two matrix random variables, constructed from different Wishart ratios, that describe the process for the two consecutive time periods before and immediately after the change in the covariance structure took place. The product moments of these constructed random variables are highlighted and set the scene for a proposed measure to enable the practitioner to calculate the run-length probability to detect a shift immediately after a change in the covariance matrix occurs. Our results open a new approach and provides insight for detecting the change in the parameter structure as soon as possible once the underlying process, described by a multivariate normal process, encounters a permanent/sustained upward or downward shift.

scholarly journals Minimax Estimation of a Normal Mean Vector for Arbitrary Quadratic Loss and Unknown Covariance Matrix

1977 ◽  
Vol 5 (4) ◽  
pp. 763-771 ◽  
Author(s):  
J. Berger ◽  
M. E. Bock ◽  
L. D. Brown ◽  
G. Casella ◽  
L. Gleser
Keyword(s):  
Covariance Matrix ◽  
Minimax Estimation ◽  
Quadratic Loss ◽  
Normal Mean ◽  
Unknown Covariance ◽  
Mean Vector ◽  
Unknown Covariance Matrix

scholarly journals Bayesian Inference of a Multivariate Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Marick S. Sinay ◽  
John S. J. Hsu
Keyword(s):  
Bayesian Inference ◽  
Regression Model ◽  
Covariance Matrix ◽  
Covariance Structure ◽  
Model Potential ◽  
Bayesian Estimator ◽  
Multivariate Normal ◽  
Matrix Logarithm ◽  
The Matrix ◽  
Posterior Moments

We explore Bayesian inference of a multivariate linear regression model with use of a flexible prior for the covariance structure. The commonly adopted Bayesian setup involves the conjugate prior, multivariate normal distribution for the regression coefficients and inverse Wishart specification for the covariance matrix. Here we depart from this approach and propose a novel Bayesian estimator for the covariance. A multivariate normal prior for the unique elements of the matrix logarithm of the covariance matrix is considered. Such structure allows for a richer class of prior distributions for the covariance, with respect to strength of beliefs in prior location hyperparameters, as well as the added ability, to model potential correlation amongst the covariance structure. The posterior moments of all relevant parameters of interest are calculated based upon numerical results via a Markov chain Monte Carlo procedure. The Metropolis-Hastings-within-Gibbs algorithm is invoked to account for the construction of a proposal density that closely matches the shape of the target posterior distribution. As an application of the proposed technique, we investigate a multiple regression based upon the 1980 High School and Beyond Survey.

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