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Consider independent observations (rı, y₁), ..., (rn, Yn) from the model Y₁ ~ Bin(rį, p) for i = 1, ..., n, where the ri are fixed constants. Using likelihood L(p) and log-likelihood 1(p) as appropriate, compute the following items. 1. Derive the maximum likelihood estimate p. 2. Write the second derivative of log-likelihood /(p). 3. Give an expression of the approximated asymptotic standard error of by plugging in the estimate p. To this end, estimate the Fisher Information Matrix by Ŷ = − 31(p)| and then s. e. (p) = √√v¹. p=p

Consider independent observations (rı, y₁), ..., (rn, Yn) from the model Y₁ ~ Bin(rį, p) for i = 1, ..., n, where the ri are fixed constants. Using likelihood L(p) and log-likelihood 1(p) as appropriate, compute the following items. 1. Derive the maximum likelihood estimate p. 2. Write the second derivative of log-likelihood /(p). 3. Give an expression of the approximated asymptotic standard error of by plugging in the estimate p. To this end, estimate the Fisher Information Matrix by Ŷ = − 31(p)| and then s. e. (p) = √√v¹. p=p

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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= Consider independent observations (r₁, y₁), ..., (rn, Yn) from the model Y₁ Bin(ri, p) for i 1, ... , n, where ther; are fixed constants. Using likelihood L(p) and log-likelihood 1(p) as appropriate, compute the following items. 1. Derive the maximum likelihood estimate p. 2. Write the second derivative of log-likelihood 1(p). 3. Give an expression of the approximated asymptotic the Fisher Information Matrix by = standard error of ô by plugging in the estimate ĝ. To this end, estimate and then s. e. (p) VE!! _2_-1(P) \ p = p др2 p=p =
Transcribed Image Text:= Consider independent observations (r₁, y₁), ..., (rn, Yn) from the model Y₁ Bin(ri, p) for i 1, ... , n, where ther; are fixed constants. Using likelihood L(p) and log-likelihood 1(p) as appropriate, compute the following items. 1. Derive the maximum likelihood estimate p. 2. Write the second derivative of log-likelihood 1(p). 3. Give an expression of the approximated asymptotic the Fisher Information Matrix by = standard error of ô by plugging in the estimate ĝ. To this end, estimate and then s. e. (p) VE!! _2_-1(P) \ p = p др2 p=p =
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