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Let X1,...,Xn be iid from Poisson(theta), Set k(theta)=exp(-theta). (a) What is the MLE of k(theta)? Is...

Let X1,...,Xn be iid from Poisson(theta), Set k(theta)=exp(-theta).

(a) What is the MLE of k(theta)? Is it unbiased?

(b) Obtain the CRLB for any unbiased estimator of k(theta).

Math   Statistics-And-Probability   
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Answer #1

Maximum Likelihood Estimator-

From theoretical point of view, the most general method of estimation known is the method of Maximum Likelihood Estimators( MLE) which was initially formulated by C.F Gauss.

Likelihood Function-

Let x1, x2,......,xn be a random sample of size n from a population with density function f(x, theta) . Then the likelihood function of the sample values x1,x2,.... xn usually denoted by L =L( theta) is given by :

(A) MLE of k(\theta) is not estimable.

(B) CRLB - Cramer -Rao lower Bound

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