Wednesday, April 16, 2003

Estimating Equations

MLE's Using an Incorrect Model

Reading

Class notes and Section 10.2

Homework

1. Let $X_1,\dots,X_n$ be a random sample that may come from a Poisson distribution with mean $\lambda$. Find the sandwich estimator of the asymptotic variance of the MLE $\widehat{\lambda} = \overline{X}$.
2. Let $g(x) = e^{-x}$ for $x > 0$ be an exponential density with mean one and let $f(x\vert\theta)$ be a $N(\theta,1)$ density. Find the value $\theta^*$ corresponding to the density of the form $f(x\vert\theta)$ that is closest to $g$ in Kullback-Liebler divergence.

Due Friday, April 18, 2003.