5. In a study of 1000 randomly selected participants, the randomized response technique described above was applied and the outcome is tabulated in Table 1. [These are fictitious data gen- erated using the R code set.seed (3); x1=rpois (500,0.5); x2=rpois (500, 3) x=c(x1, x2); table (x). This can be helpful in entering the data.] Table 1: Frequency distribution of number of drinks (alcohol or coffee) for 1000 study participants 0 1 2 3 4 5 6 7 8 9 10 11 332 226 137 125 77 52 26 16 6 1 1 1 (i) Develop code in R which finds the maximum likelihood estimator of using the Gauss- Newton and the EM algorithm. Use 100 iterations at most. (ii) Compare the convergence behavior of both algorithms in terms of dependence of initial value and number of iterations needed to reach convergence (consider convergence reached when the first 4 digits after the colon do not change any more). (iii) Provide an estimate of the Fisher information using the plug-in estimate of the iterate of at convergence and, hence, give an estimate of the standard error of 0.
5. In a study of 1000 randomly selected participants, the randomized response technique described above was applied and the outcome is tabulated in Table 1. [These are fictitious data gen- erated using the R code set.seed (3); x1=rpois (500,0.5); x2=rpois (500, 3) x=c(x1, x2); table (x). This can be helpful in entering the data.] Table 1: Frequency distribution of number of drinks (alcohol or coffee) for 1000 study participants 0 1 2 3 4 5 6 7 8 9 10 11 332 226 137 125 77 52 26 16 6 1 1 1 (i) Develop code in R which finds the maximum likelihood estimator of using the Gauss- Newton and the EM algorithm. Use 100 iterations at most. (ii) Compare the convergence behavior of both algorithms in terms of dependence of initial value and number of iterations needed to reach convergence (consider convergence reached when the first 4 digits after the colon do not change any more). (iii) Provide an estimate of the Fisher information using the plug-in estimate of the iterate of at convergence and, hence, give an estimate of the standard error of 0.
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
![5. In a study of 1000 randomly selected participants, the randomized response technique described
above was applied and the outcome is tabulated in Table 1. [These are fictitious data gen-
erated using the R code set.seed (3); x1=rpois(500,0.5); x2=rpois (500,3) x-c (x1,x2);
table (x). This can be helpful in entering the data.]
Table 1: Frequency distribution of number of drinks (alcohol or coffee) for 1000 study participants
4.
6.
8 9
6.
1
2
3
5
7
10
11
332
226
137
125
77
52 26
16
1
1
1
(i) Develop code in R which finds the maximum likelihood estimator of 0 using the Gauss-
Newton and the EM algorithm. Use 100 iterations at most.
(ii) Compare the convergence behavior of both algorithms in terms of dependence of initial
value and number of iterations needed to reach convergence (consider convergence reached
when the first 4 digits after the colon do not change any more).
(iii) Provide an estimate of the Fisher information using the plug-in estimate of the iterate of 0
at convergence and, hence, give an estimate of the standard error of 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40951aeb-9fe1-414c-ab33-d7df0b78604e%2F148a6111-bfdd-49c4-8cbc-b8e7f5ce9f07%2F61ermx8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. In a study of 1000 randomly selected participants, the randomized response technique described
above was applied and the outcome is tabulated in Table 1. [These are fictitious data gen-
erated using the R code set.seed (3); x1=rpois(500,0.5); x2=rpois (500,3) x-c (x1,x2);
table (x). This can be helpful in entering the data.]
Table 1: Frequency distribution of number of drinks (alcohol or coffee) for 1000 study participants
4.
6.
8 9
6.
1
2
3
5
7
10
11
332
226
137
125
77
52 26
16
1
1
1
(i) Develop code in R which finds the maximum likelihood estimator of 0 using the Gauss-
Newton and the EM algorithm. Use 100 iterations at most.
(ii) Compare the convergence behavior of both algorithms in terms of dependence of initial
value and number of iterations needed to reach convergence (consider convergence reached
when the first 4 digits after the colon do not change any more).
(iii) Provide an estimate of the Fisher information using the plug-in estimate of the iterate of 0
at convergence and, hence, give an estimate of the standard error of 0.
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