Discussion
Let \(M \sim W_{p}(n, \Sigma)\) and \(CC' = \Sigma\) where C is a non-singular matrix. Then \(C^{-1}MC^{-1}\) is distributed as :
Answer: C
The distribution is \(W_{p}(n, I_{p})\).
If \(M \sim W_{p}(n, \Sigma)\), then \(BMB' \sim W_{p}(n, B\Sigma B')\) for any non-singular \(B\). Taking \(B = C^{-1}\):
\[ C^{-1}\Sigma(C^{-1})' = C^{-1}CC'(C')^{-1} = I_{p} \]
The paper prints \(C^{-1}MC^{-1}\); the result as keyed holds for \(C^{-1}M(C^{-1})'\), which is the same thing when C is symmetric, for instance \(C = \Sigma^{1/2}\). The scale matrix becomes the identity, not C, \(C^{-1}\) or \(\Sigma^{-1}\).
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development