iid of f(y) 1. Data y = {41, ... , yn} are observed where y;" Gamma(4, ), with B > 0. , (a) Derive a Method of Moments e

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Iid Of F Y 1 Data Y 41 Yn Are Observed Where Y Gamma 4 With B 0 A Derive A Method Of Moments E 1 (82.86 KiB) Viewed 18 times

iid of f(y) 1. Data y = {41, ... , yn} are observed where y;" Gamma(4, ), with B > 0. , (a) Derive a Method of Moments estimator Bum for B, based on the first moment [3] (b) Is your estimator biased? If so, what is the bias? [3] (c) What is the variance of your estimator? [4] (d) Write down the log-likelihood function e(Bly). [3] (e) Derive the score function l'(Bly). [3] (f) Derive the observed Fisher Information I(B). [3] (g) Derive the expected Fisher Information E[T(B)]. [4] (h) Hence find the Maximum Likelihood Estimator ßmle for ß [3] (i) Prove that BMLE is the Minimum Variance Unbiased Estimator. [5] (Total 31 marks]