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Statistics 601, Fall 2006
Assignment 7
On the course web page under Data is a link called “Simulated Additive Error
Regression”, which you can use to obtain a file with the data shown to you in lab
as a scatterplot. The first column of the data are values of a covariate (x) and the
second column contains values of a response (y). These data were simulated from a
model of the form,
Yi = µi (β) + σ {µi (β)}θ i ,
(1)
where
µi (β) = β0 xβi 1 exp(−β2 xi )
i ∼ iid F (location/scale ) E(i ) = 0; var(i ) = 1
Using the model given in expression (1) and the given expectation function, estimate
parameters of the model and produce interval estimates for the regression parameters (i.e., the parameters in µi (β)) and, if appropriate, for θ, using the following
approaches,
1. Traditional generalized least squares for β with fixed θ and moment estimation
of σ 2 . Clearly demonstrate how you arrived at your choice for θ.
2. The Pseudo-likelihood method of Carroll and Ruppert for β and θ and moment
estimation of σ 2 .
3. Maximum likelihood assuming i ∼ iidN (0, 1) for β and σ 2 , with unscaled
profile likelihood for θ (note that this should produce the mle of θ as well).
4. Maximum likelihood for all parameters including computation of inverse information assuming i ∼ iidN (0, 1).