Let X₁, X₂, ..., Xn be a random sample from a Beta distribution with the pdf f(x; a) = axa-1 for 0 < x < 1, and zero otherwise. Which statement is correct? (1) The approximate variance of the maximum likelihood estimator of a is. (II) The approximate variance of the maximum likelihood estimator of a is (III) The approximate variance of the maximum likelihood estimator of a is α √n (IV) None of the above. Hint: The approximate variance of the maximum likelihood estimator of a parameter is , where I (0) is the Fisher information which is defined by nI(0) I(0) O (II) (IV) O (III) O (1) -E ² log f(X;0) 2020
Let X₁, X₂, ..., Xn be a random sample from a Beta distribution with the pdf f(x; a) = axa-1 for 0 < x < 1, and zero otherwise. Which statement is correct? (1) The approximate variance of the maximum likelihood estimator of a is. (II) The approximate variance of the maximum likelihood estimator of a is (III) The approximate variance of the maximum likelihood estimator of a is α √n (IV) None of the above. Hint: The approximate variance of the maximum likelihood estimator of a parameter is , where I (0) is the Fisher information which is defined by nI(0) I(0) O (II) (IV) O (III) O (1) -E ² log f(X;0) 2020
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Let X₁, X₂, ..., Xn be a random sample from a Beta distribution with the pdf
f(x; a) = axa-1 for 0 < x < 1, and zero otherwise. Which statement is correct?
(1) The approximate variance of the maximum likelihood estimator of a is.
(II) The approximate variance of the maximum likelihood estimator of a is
(III) The approximate variance of the maximum likelihood estimator of a is
α
√n
(IV) None of the above.
Hint: The approximate variance of the maximum likelihood estimator of a parameter is
, where I (0) is the Fisher information which is defined by
nI(0)
I(0)
O (II)
(IV)
O (III)
O
(1)
-E
² log f(X;0)
2020](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56efeaf7-76a0-4b65-825f-2d31d5481427%2F1bae8a3a-6158-42d1-a103-408a1163ae93%2Fatugeyd_processed.png&w=3840&q=75)
Transcribed Image Text:Let X₁, X₂, ..., Xn be a random sample from a Beta distribution with the pdf
f(x; a) = axa-1 for 0 < x < 1, and zero otherwise. Which statement is correct?
(1) The approximate variance of the maximum likelihood estimator of a is.
(II) The approximate variance of the maximum likelihood estimator of a is
(III) The approximate variance of the maximum likelihood estimator of a is
α
√n
(IV) None of the above.
Hint: The approximate variance of the maximum likelihood estimator of a parameter is
, where I (0) is the Fisher information which is defined by
nI(0)
I(0)
O (II)
(IV)
O (III)
O
(1)
-E
² log f(X;0)
2020
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