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, FatouLesbegue and Prohorov. 2) to derive, develop, and interpret maximum likelihood or minimum chisquare 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, FatouLesbegue 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 chisquare. 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 


Entreevoorwaarden  
Opmerkingen  
Opgenomen in 
