Do complete problem Suppose that independent observations r1, 22,..., rn are available from thelog-normal distribution with pdf11 (log rf(r|0) :exp(2m)'/20xon r> 0,2where 0 > 0. It can be shown that the log-likelihood ise(0) = C – n log 0 –202 L (log x;)²,where C does not depend on 0 (you do not need to prove this result). Let ôbe the MLE of 0. It also turns out to be the case that2nE{-l"(0)} =02(Again, you do not need to prove this result.)In this question, interest lies in testing Họ : 0 = 60 against Hị : 0 # 0o.(a) Show that11log (LR) = –n log(log r:)².(b) What is the asymptotic null distribution of 2 log(LR)? Explain youranswer.(c) How would you use your answer to part (b) to perform a fixed-level testof Ho of size a = 0.05? (No more calculations are needed.)(d) If 0 = 1, obtain formulae for both Wald statistics, W1 and W2.%3D

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that independent observations a1, r2,...,n are available from the log-normal distribution with pdf 1 f(r|0) = 1 (log r on r> 0, exp (27)!/20x where 0> 0. It can be shown that the log-likelihood is e(0) = C – n log 0 1 (log r.)², 202