Monthly Archives: February 2020

Derivation: Wilk’s $ \Lambda $ as $ \prod \frac{1}{1+\lambda_i} $.

Show that Wilk’s \( \Lambda \) can be represented as \[ \Lambda = \frac{|E|}{|E+H|} = \prod_{1=1}^s\frac{1}{1+\lambda_i} \], where $ \lambda_i $ is the eigenvalues of $ E^{-1}H $. Proof: \[ \frac{|E|}{|E+H|} = \frac{|E|/|E|}{|E+H|/|E|} = \frac{1}{|E^{-1}E+E^{-1}H|} = \frac{1}{|I+E^{-1}H|} \] Now suppose $ \mu $ as an eigenvalue of $ |I+E^{-1}H| $,… Read more »