Consider independent observations (ri, y₁), ... (rns yn), from the model Y,~ Bin(r,, p) for i = 1, ... , n, where the r, are fixed constants. Using likelihood L(p) and log-likelihood I(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 p by plugging in the estimate p. To -1(p) and then s. e. (p) = √v¹. p=p 4. Consider data (15,11), (20,14), (15,9), (10,7), (25,17), (15,12), (10,8). Using your formulæ, compute and write numerical estimates p, s. e. (p) and give a 95% confidence interval for p using the normal approximation. this end, estimate the Fisher Information Matrix by = == Note: To answer this question you will work by hand. Do not write in the textbox but upload a single page pdf image of your workings and results. For theoretical computations (a) to (c) you are expected to show your equations and developments in detail, simplifying as much as possible; for the numerical calculations in (d) you can use R but only write the requested results.
Consider independent observations (ri, y₁), ... (rns yn), from the model Y,~ Bin(r,, p) for i = 1, ... , n, where the r, are fixed constants. Using likelihood L(p) and log-likelihood I(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 p by plugging in the estimate p. To -1(p) and then s. e. (p) = √v¹. p=p 4. Consider data (15,11), (20,14), (15,9), (10,7), (25,17), (15,12), (10,8). Using your formulæ, compute and write numerical estimates p, s. e. (p) and give a 95% confidence interval for p using the normal approximation. this end, estimate the Fisher Information Matrix by = == Note: To answer this question you will work by hand. Do not write in the textbox but upload a single page pdf image of your workings and results. For theoretical computations (a) to (c) you are expected to show your equations and developments in detail, simplifying as much as possible; for the numerical calculations in (d) you can use R but only write the requested results.
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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Transcribed Image Text:Consider independent observations (rı, y1), ... (rns yn), from the model Y, Bin(ri, p) for i = 1, ... , n,
where the r, are fixed constants. Using likelihood L(p) and log-likelihood I(p) as appropriate, compute the
following items.
N
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 p by plugging in the estimate p. To
this end, estimate the Fisher Information Matrix by :
and then s. e.
ap²
4. Consider data (15,11), (20,14), (15,9), (10,7), (25,17), (15,12), (10,8). Using your formulæ, compute and write
numerical estimates p, s. e. (p) and give a 95% confidence interval for p using the normal approximation.
e. (p) = √v¹¹
p=p
Note: To answer this question you will work by hand. Do not write in the textbox but upload a single page pdf
image of your workings and results. For theoretical computations (a) to (c) you are expected to show your
equations and developments in detail, simplifying as much as possible; for the numerical calculations in (d) you
can use R but only write the requested results.
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Step 1: Write the given information.
VIEWStep 2: Drive the maximum likelihood estimate for p.
VIEWStep 3: Determine the second derivative of log-likelihood l(p).
VIEWStep 4: Derive an expression of the approximated asymptotic standard error of p hat.
VIEWStep 5: Construct the 95% confidence interval for p using the normal approximation.
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