y = 6, (ii) y = 25, (iii) y = 0.5. Are there any problems in finding a maximum in these cases? y=6 y=25 Value of Beta 6 Value of Beta 5 4 0.5 0.3 5 0.1 10 Iteration 15 5 20 Value of Beta 10 25 Iteration 20 15 10 5 5 15 10 20 Iteration 15 6. Here, two different starting values for 3 are chosen. Do these affect the number of iterations until convergence? y = 0.5; Bo= 0.1 0.50 Value of Beta 0.40 20 0.30 Value of Beta 2500000 1000000 0 5 y=0.5 5 10 Iteration y=0.5; Bo=0.3 10 Iteration 15 15 20 20

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 17EQ
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Numerical Maximization: Suppose we want to maximize this likelihood with respect to 3:
TI 1
L(B|y₁, yn) = II
i=1
-yi/B
Transcribed Image Text:Numerical Maximization: Suppose we want to maximize this likelihood with respect to 3: TI 1 L(B|y₁, yn) = II i=1 -yi/B
5. Below are the results from running Newton's algorithm in R. when n = 10 with the starting point Bo
y = 6, (ii) y = 25, (iii) y = 0.5. Are there any problems in finding a maximum in these cases?
y=25
y=6
Beta
Value
9
Value of Beta
5
4
3
2
0.5
0.3
5
0.1
10
Iteration
15
5
20
Beta
10
Value
25
Iteration
20
15
10
5
5
15
10
20
Iteration
15
Value of Beta
0.50
0.40
T
20
6. Here, two different starting values for 3 are chosen. Do these affect the number of iterations until convergence?
y=0.5; Bo= 0.1
y=0.5; Bo=0.3
0.30
Beta
Value
2500000
1000000
5
0
5
y=0.5
10
10
Iteration
Iteration
2 when (i)
15
15
20
20
Transcribed Image Text:5. Below are the results from running Newton's algorithm in R. when n = 10 with the starting point Bo y = 6, (ii) y = 25, (iii) y = 0.5. Are there any problems in finding a maximum in these cases? y=25 y=6 Beta Value 9 Value of Beta 5 4 3 2 0.5 0.3 5 0.1 10 Iteration 15 5 20 Beta 10 Value 25 Iteration 20 15 10 5 5 15 10 20 Iteration 15 Value of Beta 0.50 0.40 T 20 6. Here, two different starting values for 3 are chosen. Do these affect the number of iterations until convergence? y=0.5; Bo= 0.1 y=0.5; Bo=0.3 0.30 Beta Value 2500000 1000000 5 0 5 y=0.5 10 10 Iteration Iteration 2 when (i) 15 15 20 20
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