NMAK14007U Asymptotic theory

Asymptotic mathods in statistics are approximation results for the distributions of estimators and test statistics, valid as the number of observations tend to infinity.  The basic asymptotic result is the Central Limit Theorem, which concerns sums of independent or weakly dependent stochastic variables.  However, interesting constructions in statistics are usually not sums, at least not in any transparent way. So a certain amount of work is needed to identify relevant sums of variables, and to make sure that these sums indeed control the behaviour of  the constructions of interest.
 
The course will focus on rigorous derivations of asymptotic results for M-estimators, a very large class encompassing most estimation procedures in common use. We will also consider several subclasses of M-estimators in detail.  The course will also contain an introduction to higher order asymptotic theory, relying on modifications of the underlying CLT.  If time permits we will explore the connection between the asymptotic results and   the arguments behind the use of informations criteria in model selection