We will use the two ¡­

We will use the two final Mondays (18th and 25th of May) before the exam project to "look back", discussing central themes of the course, considering some of the "methods in action" illustrations, etc.

A final version of the "Notes & Exercises" file will be finished & uploaded shortly.

Here's a final exercise for us to go through.

F: (a) When there's only one extra parameter, from narrow to wide, show that AIC is large-sample equivalent to including \gamma if |D_n/\kappa| \ge \sqrt(2), in notation of Chs. 5 and 6. (b) Show that Pr(AIC selects wide) converges to pow(delta/kappa), where pow(u) = Pr(|N(u,1)| \ge sqrt(2)), and that the 50-50 line, where AIC selects narrow or wide with the same probability 1/2, is at |delta| = kappa c0, with c0 = 1.408. (c) Set up a simple simulation experiment as follows, intended at having about 50-50 balance between narrow and wide. The narrow model is y = beta0 + beta1 x + noise, the wide is y = beta0 + beta1 x + beta2 x^2 + noise, with x taken random from N(0,1) and noise with standard deviation 1. Show that if beta1 = (c0/sqrt(2))/sqrt(n), then AIC is in the limit in the 50-50 balance situation. Simulate situations from such a model, say with beta0 = 3 and beta1 = 1, and compute estimates and "quiet scandal" type confidence intervals for mu(x0) = E(Y | x0), with x0 = 2.0. Comment on your findings. Study also compromise estimators using smooth AIC weights.