(1) For a random sample of size n finite, The variance of theMaximum Likelihood

Question

(1) For a random sample of size n finite, The variance of theMaximum Likelihood Estimator equals the Cramer-Rao bound. (True/Flase) . (2) In the Bayesian approach to parameter estimation, theparameter to estimate is assumed to be random. (True/False) . (3) The estimator provided by the method of moments is alwaysunbiased. (True/False) (1) For a random sample of size n finite, The variance of theMaximum Likelihood Estimator equals the Cramer-Rao bound. (True/Flase) . (2) In the Bayesian approach to parameter estimation, theparameter to estimate is assumed to be random. (True/False) . (3) The estimator provided by the method of moments is alwaysunbiased. (True/False) (True/False)

Explanation / Answer

1) True For a random sample size n finite, the variance of the mleequals the cramer-Rao bound is true. 2) True In the Bayesian approach to parameter estimation, theparameter is assumed to be indepedent and random vectors. 3) True The estimator provided by the method of moment almost alwaysprovide asymptotically unbiased estimators.

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