id = 1. Data y = {41,..., yn} are observed where yi! Gamma(4,), with B > 0. (a) Derive a Method of Moments estimator Bum

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Id 1 Data Y 41 Yn Are Observed Where Yi Gamma 4 With B 0 A Derive A Method Of Moments Estimator Bum 1 (44.84 KiB) Viewed 17 times

id = 1. Data y = {41,..., yn} are observed where yi! Gamma(4,), with B > 0. (a) Derive a Method of Moments estimator Bum for B, based on the first moment of fly). [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 (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 Bmle for B [3] (i) Prove that BMLE is the Minimum Variance Unbiased Estimator. [5] [Total 31 marks]