Advanced Asymptotic Statistics

Faculteit Science and Engineering
Jaar 2017/18
Vakcode WMMA16009
Vaknaam Advanced Asymptotic Statistics
Niveau(s) master
Voertaal Engels
Periode semester I a
ECTS 5
Rooster rooster.rug.nl

Uitgebreide vaknaam Advanced Asymptotic Statistics
Leerdoelen The aim of the course is that students obtain insight on the role of asymptotic theory in statistical estimation theory.

The student is able
1) to derive and apply convergence in various modes from basic measure theoretic Theorems such as Portmantau, Fatou-Lesbegue and Prohorov.
2) to derive, develop, and interpret maximum likelihood or minimum chi-square inference methods for a number of estimation problems
3) to derive and apply necessary and sufficient conditions for the Laws of Large Numbers and versions of the Central Limit Theorem
4) to determine necessary and sufficient conditions for consistent and efficient estimators for a wide scope of problems
Omschrijving In this course the properties of probabilistic modes of convergence and their partial converses are analyzed in detail from measure theoretic theorems such as Portmantau, Fatou-Lesbegue and Prohorov. Three Laws of Large Numbers and two versions of the Central Limit Theorem are proven, discussed and illustrated. To obtain a wider scope of application of these theorems, we introduce the Slutsky and Delta theorems. This forms the mathematical basis of regularity assumptions making statistical estimation possible based on maximum likelihood and minimum chi-square.
Throughout the course we provide examples as well as counter examples to deepen insight.
Uren per week
Onderwijsvorm Hoorcollege (LC), Werkcollege (T)
(Assessment takes place through homework assignments and written exam according to Final = 0.10 x max(HW1, ET) + 0.10 x max(HW2, ET) + 0.10 x max(HW3, ET) + 0.7 x ET only if ET>=5.0 otherwise Final = ET, where HWi is homework grade for ith homework set, ET final exam grade)
Toetsvorm Opdracht (AST), Schriftelijk tentamen (WE)
(will be announced as soon as possible)
Vaksoort master
Coördinator dr. W.P. Krijnen
Docent(en) dr. W.P. Krijnen
Verplichte literatuur
Titel Auteur ISBN Prijs
A Course in Large Sample Theory, Chapman & Hall, 1996 Thomas S. Ferguson
Entreevoorwaarden
Opmerkingen
Opgenomen in
Opleiding Jaar Periode Type
MSc Mathematics  (Science, Business and Policy with Statistics and Big Data) - semester I a keuzegroep
MSc Mathematics  ( Statistics and Big Data) - semester I a keuzegroep