exercises for Mon Mar 2

On Mon Feb 24 we went through various exercises, including Scheffe's lemma, and Emil Stoltenberg Exam 2017 no 1, with variance stabilising transformations etc. I then went through Section 13, on sample quantiles and their joint multinormal limit distribution, and this is the single section inside Ferguson's Part III that is defined as core curriculum.  I will also write out some more details qua Nils Exercises in the Nils Collection.

Our forum thanks Ingrid D?hlen for en betimelig og inspirert vits, and Dennis Christensen for an impromptu two-minute lecture to us, on how Euler used the \log(x + \sqrt{1+x^2}) function and its derivative to put up the eternally magical equation

e^{i \pi} + 1  = 0.

https://www.facebook.com/groups/1589206911336271/permalink/2544622505794702/

Next week we start with Part IV, with likelihood inference topics.

For Mon Mar 2, work through Ferguson Exercises 1, 2, 5 from Section 1, 1 from Section 2, 4 from Section 3, 4 from Section 4.

Also, for X_1, ..., X_n i.i.d. from the normal distribution, work out the limit distribution for the interquartile range, R_n = upper quartile minus lower quartile. Construct a robust estimator for the standard deviation \sigma based on R_n. How much does the estimator, compared to the traditional model based estimator for \sigma, if the normal model is actually correct?