Kursens poäng (högskolepoäng, hp) 7.5
Kursen ges normalt Every second year
Tillhör institution Matematiska vetenskaper
Dragi Anevski, email@example.com
tel +46 (0)730 794241
The goal of the course is to provide a set of tools and results used in modern inference theory. Many of the key concepts are applied to modern survival analysis, density estimation, spectral density estimation, and thus the course can also be seen as an introduction these topics. We will also cover some nonstandard topics, such as empirical process theory for stationary data, and estimation of the spectral measure of stationary processes. (The chapter numbering below refers to Van der Vaart's book).
INTRODUCTION (Chapter 1),
WEAK CONVERGENCE AND EMPIRICAL PROCESS THEORY.
Weak convergence (Chapter 18),
Empirical processes (Chapter 19),
Functional differentiability (Chapter 20),
*Quantiles and order restrictions (Chapter 21),
*L-statistics (Chapter 22),
Bootstrap (Chapter 23),
Nonparametric density estimation(Chapter 24),
*Empirical and partial sum process for long range dependent data.
*The empirical spectral process.
M-ESTIMATORS AND SEMIPARAMETRIC METHODS
M and Z-estimators (Chapter 5)
*Contiguity and limit of experiments (parts of Chapters 6,7 and 8).
Main course book is Van der Vaart's book (recommended buying), complemented with some papers. The other books are complementary reading.
Van der Vaart (1998), "Asymptotic Statistics", Cambridge University Press. (main source)
Van der Vaart and Wellner (1996), "Weak convergence and empirical processes", Springer.
Billingsley (1968), "Convergence of Probability Measures", Wiley.
Dehling and Taqqu (1989), "The empirical process of some long-range dependent sequences with an application to U-statistics", Annals of Statistics no 17, 1767--1783.
Taqqu (1975), "Weak convergence to fractional Brownian motion and to the Rosenblatt process", Z. Wahrsch. Verw. Gebiete no 50, 53-83 (1979).