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iid Let Y1, Y2, Y3, ..., Yn N(µ, o2), where o² = 25 is known. c distribution of Z := Jin where u is the MLE. Hint: what is ribution of i?

iid Let Y1, Y2, Y3, ..., Yn N(µ, o2), where o² = 25 is known. c distribution of Z := Jin where u is the MLE. Hint: what is ribution of i?

MATLAB: An Introduction with Applications
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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Solve parts 1 and 2 of the question below. Show all work.

 

iid Let Y1, Y2, Y3, ..., Y, N(µ, 0²), where o? = 25 is known. 1. Find the asymptotic distribution of Z := where u is the MLE. Hint: what is the asymptotic distribution of i? 2. Suppose now we do not know o? and instead plug in the MLE estimator ô? :E(Yi – î)² to obtain Z := Is the asymptotic distribution still N(0, 1)? If yes, why? (hint: what do we know about consistency of MLES? Slutsky's theorem?).
Transcribed Image Text:iid Let Y1, Y2, Y3, ..., Y, N(µ, 0²), where o? = 25 is known. 1. Find the asymptotic distribution of Z := where u is the MLE. Hint: what is the asymptotic distribution of i? 2. Suppose now we do not know o? and instead plug in the MLE estimator ô? :E(Yi – î)² to obtain Z := Is the asymptotic distribution still N(0, 1)? If yes, why? (hint: what do we know about consistency of MLES? Slutsky's theorem?).
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