# MLE

Not what you're looking for? Search our solutions OR ask your own Custom question.

Verify that ?(^) maximizes the likelihood function L(?; y) if and only if it also maximizes the log of the likelihood function, InL(?; y). That is, prove that

L(?(^); y)>L(?(~);y) if and only if lnL(?(^);y)>lnL(?(~);;y)for all ?(~);??(^)

Please see attached.

Â© BrainMass Inc. brainmass.com October 1, 2022, 5:34 pm ad1c9bdddfhttps://brainmass.com/statistics/estimation-theory/maximizes-likelihood-function-37541

#### Solution Preview

see attachment

Verify that Î¸(^) maximizes the likelihood function L(Î¸; y) if and only if it also maximizes the log of the likelihood function, InL(Î¸; y). ...

#### Solution Summary

Verify that ?(^) maximizes the likelihood function L(?; y) if and only if it also maximizes the log of the likelihood function, InL(?; y). That is, prove that

L(?(^); y)>L(?(~);y) if and only if lnL(?(^);y)>lnL(?(~);;y)for all ?(~);??(^)

$2.49