Biostat 200C Homework 4

Due May 23 @ 11:59PM

1 Q1. ELMR Excercise 7.5 (p150)

(60pts, each 10pts)

2 Q2. Moments of exponential family distributions

(20pts, each 10pts)

Show that the exponential family distributions have moments \[\begin{eqnarray*} \mathbb{E}Y &=& \mu = b'(\theta) \\ \operatorname{Var}Y &=& \sigma^2 = b''(\theta) a(\phi). \end{eqnarray*}\]

3 Q3. Score and information matrix of GLM

(20pts, each 10pts)

Derive the gradient (score), negative Hessian, and Fisher information matrix (expected negative Hessian) of GLM.

4 Q4. ELMR Exercise 8.1 (p171)

(25pts, each 5pts)

5 Q5. ELMR Exercise 8.4 (p172)

(35pts, each 5pts)

6 Q6. ELMR Exercise 8.5 (p172)

(90pts, each 10pts)