Let be a random sample from the density function given by,

0 otherwise, for known r.

Find a sufficient statistic and maximum likelihood for . Argue that the maximum likelihood estimator is also sufficient for

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- Aug 18th 2009, 05:05 AMpanda*Sufficiency and Maximum Likelihood.
Let be a random sample from the density function given by,

0 otherwise, for known r.

Find a sufficient statistic and maximum likelihood for . Argue that the maximum likelihood estimator is also sufficient for

- Aug 18th 2009, 08:13 AMmatheagle
By the factorization theorem

or any multiple of it is suff for

we get that from the likelihood function. - Aug 19th 2009, 03:44 PMpanda*
Then what's the maximum likelihood for theta? Is it possible to illustrate a few steps to kick start? Thank you!