exercises for Mon Mar 9

1. On Mon Mar 2 we rounded off Part III from Ferguson, with a bit more material on sample quantiles, and we started on Part IV, with introductory discussions of maximum likelihood etc. We also did *some* of the listed exercises from Ferguson, and will do more next week. 

2. The course curriculum will be detailed separately, and soon, but consists of five parts -- Parts I, II, III, IV roughly corresponding to these parts of Ferguson's book, and Part V to be on *empirical processes*, with separate material to come from Nils. 

3. For Mon Mar 9, start with the following exercise. First, write out clearly how to form a 95 percent confidence interval for the population median, based on a sample of n datapoints. This involves estimating the limit distribution standard deviation 0.50/f(\mu), and for this ingredient use the kernel density estimate, \hat f(x) = n^{-1} \sum h^{-1} dnorm(h^{-1}(x_i - x)), with default bandwidth taken to be h = 1.059 \sd(x) / n^{1/5}. Then do this!, for the two datasets placed at the course website named birthweight-boys and birthweight-girls (for 480 boys and 548 girls born in Oslo, I believe just after the year 2000). The files give birthweights in grams, but please convert to kilograms. 

Then do this also for the nine deciles, with quantiles q = 0.10, 0.20, ..., 0.80, 0.90, and make a plot with the estimated quantiles with 0.95 band, for the boys and the girls. 

Then other and smaller (?) exercises, this time from Ferguson: Section 1: 4, 5. Section 2: 1. Section 3: 4. Section 5: 4.