Applications of quadratic minimisation problems in statistics

Albers et al. (2010) [2] showed that the problem subject to where  is positive definite or positive semi-definite has a unique computable solution. Here, several statistical applications of this problem are shown to generate special cases of the general problem that may all be handled within a general unifying methodology. These include non-trivial considerations that arise when (i)  and/or  are not of full rank and (ii) where  is indefinite. General canonical forms for  and  that underpin the minimisation methodology give insight into structure that informs understanding.