Ellevte roman, bok atten

1. Wed Apr 3 we discussed the basics of FIC: the master theorem about the behaviour of muhat(S); the consequent expressions for risk functions (mean squared error, i.e. variance plus squared bias); how to estimate these. The model is selected corresponding to the smallest estimated risk. We also went through different numerical methods for calculating the tolerance level kappa(a1)/rootn for the log-linear expansion model of Exam stk 4160 2009 Exercises 1-2.

2. Exercise for Wed Apr 10: Access again the car sales data of (xi,yi), of Exam stk 4020 2012 Exercise 2. Consider the wide model where yi = m(xi)*epsi, where m(x) = exp(beta0 + beta1 x + beta2 xsquared) and the epsi are iid Gamma(c,c). Take the narrow model to have m(x) = exp(beta1 x). Fit now each of the four models corresponding to pushing beta0 and beta2 in and out. For each estimate the focus paramaters mu1 = m(x0) for x0 = 5 years and mu2 = the half-time of a car, where m(mu2) = 0.5. Compute AIC, BIC, and FIC scores, and discuss your findings. Construct FIC plots for mu1 and mu2. Note: Translate the y-data here from percentages to ordinary ratios between zero and one -- otherwise the natural narrow model would need to take the form corresponding to m(x) = 100*exp(beta1 x), i.e. exp(beta0) = 100 above. Both analyses would be fine, of course, but it is a bit simpler to carry out the analysis using ratios and hence exp(beta0) = 1 i.e. beta0 = 0 for the narrow model.