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
icon
Related questions
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).
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).
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman