Asymptotic Properties of MLES ... 'F Let X₁, X2, X3, Xn be a random sample from a distribution with a parameter 8. Let ML denote the maximum likelihood estimator (MLE) of 0. Then, under some mild regularity conditions, 1. ML is asymptotically consistent, i.e., - lim P(|ÔML − 0| > e) = 0. 11-700 2. ML is asymptotically unbiased, i.e., lim E[ML] = 0. 12-00 precisely, the random variable 3. As n becomes large, ML is approximately a normal random variable. More ML-0 √Var(OML) converges in distribution to N(0, 1).

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
i need the answer quickly
Asymptotic Properties of MLES
Let X1, X2, X3,
Xn be a random sample from a distribution with a
1...
parameter 6. Let OML denote the maximum likelihood estimator (MLE) of 0.
Then, under some mild regularity conditions,
1. OML is asymptotically consistent, i.e.,
lim P(ÔML - 0| > e) = 0.
2. OML is asymptotically unbiased, i.e.,
lim E ÔML] =
3. As n becomes large, OML is approximately a normal random variable. More
precisely, the random variable
V Var(ÔML)
converges in distribution to N(0, 1).
Transcribed Image Text:Asymptotic Properties of MLES Let X1, X2, X3, Xn be a random sample from a distribution with a 1... parameter 6. Let OML denote the maximum likelihood estimator (MLE) of 0. Then, under some mild regularity conditions, 1. OML is asymptotically consistent, i.e., lim P(ÔML - 0| > e) = 0. 2. OML is asymptotically unbiased, i.e., lim E ÔML] = 3. As n becomes large, OML is approximately a normal random variable. More precisely, the random variable V Var(ÔML) converges in distribution to N(0, 1).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 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