Assignment one presentation

Question 2.5 (a)-(d)

by Hao Ding

Derive Newton-Raphson Update

•A Starting point

•First derivative of Log – Likelihood

•Second derivative of Log – Likelihood

Slide 2

Newton-Raphson: Derivation

Slide 3

Newton-Raphson: Derivation

Slide 4

Newton-Raphson: Implementation

Slide 5

solve(gpp) %*% gp

Fisher Scoring

•Compute the Fisher Information

•Using Fisher Information to replace second derivative

Slide 6

Newton VS Fisher Scoring

•Implementation cost• Fisher Scoring is easier to implement: less computational cost

•Performance

Slide 7

Estimate Standard Error of MLEs

• .

•Evaluate the Fisher Information with MLEs

•The standard errors are the diagonal terms of the inverse of Fisher Information

Slide 8