Abstract
In this paper, we consider the estimation of a scatter matrix under entropy loss, quadratic loss, when the samplesx(1),...x(n) are i.i.d. andx(1)∼ECp(μ,Σ,f). With respect to entropy and quadratic losses, we obtain the best estimator ofΣ having the formαSx as well as having the formTxΔTx′, whereSx,Tx andΔ are given in the text, and obtain the minimax estimator ofΣ and the best equivariant estimator ofΣ with respect to the triangular transformations groupLT+(p) (the group consisting of lower triangular matrices with positive diagonal elements). Some related discussion are given as its generalizations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
