Exercises for Wed Feb 13

1. I have now more or less finished Ch 2 (i.e. the curriculum active parts of that chapter), with AIC, AIC^*, cross-validation, regression models, Jhat, Khat, sandwich estimator, etc., but will spend a bit more time on Wed Feb 13 to sum up things.

2. I've placed com12a on the course website, with code doing the essence of Nils Exercise 2.

3. Exercises for Wed Feb 13 are as follows.

(a) Simulate say 1000 versions for Exercise 2, to track the probabilities for the different models winning the AIC competition.

(b) For Exercise 2, work out how not only the Jhat matrix can be computed, but also the Khat matrix, and hence the sandwich matrix.

(c) Suppose the true density for a certain lifetime distribution is g(y) = 0.5 dgamma(y,a1,b1) + 0.5 dgamma(y,a2,b2), with (a1,b1) equal to (1.238,0.061) and (a2,b2) equal to (4.504,0.111). For the two-parameter candidate models (i) gamma, (ii) Weibull, (iii) Gompertz, work out the least false parameters, and also the resulting minimum Kullback-Leibler distances KL(g, f_\leastfalse). Draw the relevant densities in a diagram.

(d) Go to Gerda Claesken's site for our book, find the football data, with 254 matches, with rows of the type (team A goals, team B goals, team A fifa score, team B fifa score), with the fifa scores valid three weeks before the tournaments. Build, fit, assess, compare some Poisson rate models for these data.