Let $Y$ be independent and identically distributed normal with mean $2\mu$ and variance $16$.
Show that $\frac{\bar y}{2}$ is the maximum likelihood estimator of $\mu$.
$\begingroup$
$\endgroup$
1
1 Answer
$\begingroup$
$\endgroup$
1
You can use invariance property of Maximum Likelihood estimator:
http://en.wikipedia.org/wiki/Maximum_likelihood
If alpha_hat=g(theta_hat) then theta_hat is MLE for alpha_hat.
And notice that 1/2 is jacobian for transformation of alpha=2*theta and average of y is MLE for myy.
-
$\begingroup$ Why does anyone need to consider the Jacobian? There is no integration over the parameters. $\endgroup$– whuber ♦Feb 10, 2014 at 17:35
self-study. Please add theself-studytag and review its tag wiki info. With that in mind, what have you tried, and where does your difficulty lie? $\endgroup$