Estimation in the multivariate context when the number of observations available is less than the number of variables is a classical theoretical problem. In order to ensure estimability, one has to assume certain constraints on the parameters. A method for maximum likelihood estimation under constraints is proposed to solve this problem. Even in the extreme case where only a single multivariate observation is available, this may provide a feasible solution. It simultaneously provides a simple, straightforward methodology to allow for specific structures within and between covariance matrices of several populations. This methodology yields exact maximum likelihood estimates.
Maximum likelihood estimation under constraints for estimation in the Wishart class
of distributions, is considered. It provides a unified approach to estimation in a variety of
problems concerning covariance matrices. ...
Chae, Younghwan; Wilke, Daniel Nicolas(Elsevier, 2017-12)
The digital age has significantly impacted our ability to sense our environment and infer the state or status of equipment in our environment from the sensed information. Consequently inferring from a set of observations ...
Majozi, Nobuhle P.; Mannaerts, Chris M.; Ramoelo, Abel; Mathieu, Renaud; Mudau, Azwitamisi E.; Verhoef, Wouter(MDPI Publishing, 2017-03-24)
Knowledge of evapotranspiration (ET) is essential for enhancing our understanding of
the hydrological cycle, as well as for managing water resources, particularly in semi-arid regions.
Remote sensing offers a comprehensive ...