4. Let X1,., Xn be iid with pdf f(x; 0). Suppose that we test Ho 0 = 0o ver- sus H1 :0 + 0o using the LR statistic %3D .... Tn = log L(6) – log L(0), where 0 is the MLE of 0. Show that if n-Tn 40 under Ho, then the sequence of tests is consisitent (i.e., under H1 the power of the test tends to one as n → o0).
4. Let X1,., Xn be iid with pdf f(x; 0). Suppose that we test Ho 0 = 0o ver- sus H1 :0 + 0o using the LR statistic %3D .... Tn = log L(6) – log L(0), where 0 is the MLE of 0. Show that if n-Tn 40 under Ho, then the sequence of tests is consisitent (i.e., under H1 the power of the test tends to one as n → o0).
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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Question
![4. Let X1,., Xn be iid with pdf f(x; 0). Suppose that we test Ho : 0 = Oo ver-
sus H1 :0 + 0o using the LR statistic
Tn = log L(0) –- log L(00),
where 0 is the MLE of 0. Show that ifn-Tn 4 0 under Ho, then the sequence of
tests is consisitent (i.e., under H1 the power of the test tends to one asn → 0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F160bf88a-3e12-47ea-82d8-8bf82c08a312%2Fdeb353fd-4246-4ced-97cf-661810ac729b%2Fual1cu8_processed.png&w=3840&q=75)
Transcribed Image Text:4. Let X1,., Xn be iid with pdf f(x; 0). Suppose that we test Ho : 0 = Oo ver-
sus H1 :0 + 0o using the LR statistic
Tn = log L(0) –- log L(00),
where 0 is the MLE of 0. Show that ifn-Tn 4 0 under Ho, then the sequence of
tests is consisitent (i.e., under H1 the power of the test tends to one asn → 0).
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