exercises for Mon Feb 17

1. On Mon Feb 10 we went through various Nils Collection Exercises, 25, 26, 27 (on the Borel-Cantelli matters), 43 (a.s. convergence, strong consistency), 53 (characteristic functions, characterising normality). We also discussed central aspects of Ferguson's Part II, often having to do with (i) establishing limiting joint normality of relevant components of a given problem, e.g. various sample means, and (ii) applying the delta method to read of  limiting normality for certain functions of these start ingredients. 

2. I've updated the Nils Collection, now Version D, as of 11-Feb-2020, so far 51 pages. Print out & enjoy. 

3. For next week, we'll go through further themes and issues from Ferguson's Part II, including the Pearson chi-squared (from his glorious paper of 1900, actually), limit distribution for the empirical correlation coefficient; in this connection, check also Nils Exercise 67, which contains more information than in Ferguson.

We'll soon enough be rounding off all of Part II, and from Part III only the section on limit distributions for sample quantiles will be inside the curriculum -- which means that we're not far off from Part IV, where we go into maximum likelihood, Bayes, deviance, the Wilks theorem, and confidence cuves. 

4. Exercises for next Monday: work through (i) Stoltenberg Exam, Exercise 3, on Lindeberg things, and (ii) Nils Exercises 65, 66.