Study Programmes 2016-2017
MATH0065-1  
Probability and statistics IV
Duration :
30h Th, 10h Pr, 20h Mon. WS
Number of credits :
Master in mathematics (120 ECTS)8
Master in mathematics (60 ECTS)8
Lecturer :
Yvik Swan
Language(s) of instruction :
English language
Organisation and examination :
Teaching in the second semester
Units courses prerequisite and corequisite :
Prerequisite or corequisite units are presented within each program
Learning unit contents :
A course in large sample theory
  • Modes of convergence
  • Partial converses
  • Convergence in law
  • Laws of Large Numbers
  • Central Limit Theorems
  • Probability distances
  • Stein's method
  • Slutsky lemmas
  • Delta method
  • Sample correlation coefficient
  • Pearson ChiSquared
Learning outcomes of the learning unit :
At the end of the course the student shall understand and master the proofs  of the main asymptotic statements used in statistical practice.
Prerequisite knowledge and skills :
The material thought in Bachelor in Mathematics at ULg (particularly the courses Statistics and Probability I, II, and III, Analysis I and II as well as linear algebra). 
Planned learning activities and teaching methods :
Ex cathedra classes as well as exercise sessions.
Mode of delivery (face-to-face ; distance-learning) :
Face-to-face
Recommended or required readings :
Main reference: Ferguson, Thomas Shelburne. A course in large sample theory. Vol. 49. London: Chapman & Hall, 1996.
Other reference: Nourdin, Ivan, and Giovanni Peccati. Normal approximations with Malliavin calculus: from Stein's method to universality. Vol. 192. Cambridge University Press, 2012.
Assessment methods and criteria :
Oral examination for the theory, written examination for the practical. Each counts for half the final grade. 
Work placement(s) :
Organizational remarks :
Course taught in English; examination in French or in English. 
Contacts :
Université de Liège Département de Mathématique - zone polytech 1 12 allée de la découverte Bât. B37 pkg 33a B-4000 Liège Office : B37 0/68