Title:  Course Large Deviations and Course Introductory Course to Time Series Analysis 
Organisation  AIOnetwerk Stochastiek zie ook: http://www.cs.vu.nl/~aad/aio.html (A.W. van der Vaart (), tel: 0204447697, J.H.J. Einmahl ( ), tel: 0402472499). 
Lecturers:  Frank den Hollander (first course) Thomas Mikosch (second course) 
Time and place:  Fall 97 We have planned the dates: September 5 and 19, October 3, 17 and 31*, November 14 and 28, December 12. (*The probability session of 31 October will be moved to 21 November, in Lunteren.) The morning session will be probability and the afternoon session will be statistics. As usual the courses consist of eight lectures of two hours each, given on eight Fridays. The courses will probably be given in Utrecht, in the Academiegebouw, Domplein, room 10. Morning and afternoon sessions are planned for 10.4512.30 and 13.3015.15, respectively. A final announcement will follow. 
The theory of large deviations deals with the computation of `small' probabilities, away from the central limit theorem. The reason for studying these probabilities is that they come up in a wide variety of situations, e.g. the study of functionals of random processes, the calculation of tail properties for sums of weakly dependent random variables, error estimates, etc. Large deviation theory has proved to be the crucial tool in handling many questions in statistics, probability and statistical mechanics.
The course will have three parts:
References:
J.D. Deuschel and D.W. Stroock, Large Deviations, Academic Press, Boston, 1989.
J.A. Bucklew, Large Deviation Techniques in Decision, Simulation, and Estimation, Wiley, New York, 1990.
A. Dembo and O. Zeitouni, Large Deviation Techniques and Applications, Jones and Bartlett Publishers, Boston, 1993.
Abstract: Thomas Mikosch (RUG) ()
By now, time series analysis is one of the well established theories in probability theory and mathematical statistics with applications in various fields such as hydrology, meteorology, finance, astronomy, economics. The stochastic model underlying it is mostly assumed to be a stationary discretetime process. The aim of the analysis is to detect the dependence structure in the series, to fit an appriate model and to predict future values in the series. This is done in the time or frequency domain. The first method is based on considerations of the autocorrelations and autocovariances. The second one uses Fourier analytic methods; it is also called spectral analysis.
The analysis of time series is mostly based on Hilbert space techniques. They allow one to represent a stationary process as a stochastic integral with trigonometric functions as integrands. Thus a stationary process, to a first approximation, can be understood as a sinosoid with random coefficients. The order of magnitude of those coefficients is discribed by the spectral distribution function and its density. The course will give a gentle introduction to modelling of time series both in the frequency and time domain, stressing more the understanding of the models than the discussion of technical details. Classical ARMA processes (=autoregressive moving average processes) allow us to give insight into the structure of more complicated models. ARMA models will serve as prime examples for developing a spectral and time domain analysis which is accompanied by an introduction to the statistical tools for fitting data. Prediction of times series is one of the main issues and will be described in detail.
In addition to the basics of classical time series modelling the following recent issues of interest will be discussed:
Recommended references are:
Brockwell, P.J. and Davis, R.A. (1991) {Time Series: Theory and Methods,2nd~edition. Springer, New York.
Brockwell, P.J. and Davis, R.A. (1996) { Introduction to Time Series and Forecasting.} Springer, New York.
The first reference is an introduction to time series analysis for a mathematically oriented person, the second one is for the more applied person who is interested in how things work, but does not ask why.
Title:  Course Statistical Modelling of Medical Data and Brownian Motion and the Funtional CLT 
Organisation  AIOnetwerk Stochastiek (A.W. van der Vaart (), tel: 0204447697, J.H.J. Einmahl ( ), tel: 0402472499). 
Lecturers:  Hans van Houwelingen (first course) Gerard Hooghiemstra (second course) 
Time and place:  Spring 97 We have planned the dates: January 23, February 6 and 20, March 6 and 20, April 1 and 25 May 2. The morning session will be statistics and the afternoon session will be probability. As usual the courses consist of eight lectures of two hours each, given on eight Fridays. The courses will probably be given in Utrecht, in the Academiegebouw, Domplein, room 10. Morning and afternoon sessions are planned for 10.4512.30 and 13.3015.15, respectively. A final announcement will follow. Possible late changes in the schedule will be communicated by email and are accessible via the WWW page of A.W. van der Vaart (http://www.cs.vu.nl/~aad). 
Contact:  L. de Haan (EUR), 010  408 1258, () A.W. van der Vaart (VUA), 020  444 7697, () 
References:
J.C. van Houwelingen, S. le Cessie, Predictive value of statistical models, Statistics in Medicine 9, 13031325, 1990.
S. le Cessie, H.C. van Houwelingen, Testing the fit of a regression model via score tests in random effects models, Biometrics 51, 600614, 1995
H.C. van Houwelingen, J. Thorogood, Construction, validation and updating of a prognostic model for kidney graft survival, Statistics in Medicine 14, 19992008, 1995
P.J.M. Verweij, H.C. van Houwelingen, Crossvalidation in survvial analysis, Statistics in Medicine 12, 23052314, 1993
J.J. HowingDuistermaat, B.H.F. Derkx, F.R. Rosendaal, H.C. van Houwelingen, Testing familial aggregation, Biometrics 51, 12921301, 1995
Abstract: Gerard Hooghiemstra (TUD) ()
This course is on Brownian motion and the Functional Central Limit Theorem. (FCLT).
We start with an introduction to Brownian motion involving: a full proof of continuity of paths, reflection principle, calculation of distributions of funtionals (by various methods, including exponential martingales). As reference we take the book of Freedman.
In connection with the above topic I intend to treat two FCLT's with applications:
References:
Freedman, D. Brownian Motion and Diffusion. Holden Day, 1971, ISBN 0816230242
Pollard, D. Convergence of Stochastic Processes. Springer Verlag , 1984, ISBN 0387909907
Groeneboom, P., Hooghiemstra, G. and Lopuhaa, H. P. Asymptotic normality of the L_1 error of the Grenander estimator. Report 9701, TWI, TUDELFT.
Title:  Course Measure theory, martingales and stochastics integrals. 
Organiser:  L. de Haan () 
Time and place:  OctoberDecember 1997, EUR 
Aim:  The purpose is to enable PhD students in e.g. finance to deal with martingales and stochastic integrals 
Contents:  As above. There are extensive exercise sessions 
Literature:  David Williams: Probability with martingales. Cambridge Univ. Press 1991. 
Prerequisites:  regular course in probability and statistics at the intermediate level (as in the program of Econometrics). 
Title:  Course Semiparametric Models 
Lecturers:  prof. dr. C.A.J. Klaassen () and dr. A.J. van Es () 
Time and place:  Department of Mathematics, University of Amsterdam Plantage Muidergracht 24, Amsterdam The exact time is not yet planned, but it will be in our second trimester (december  march) 
Aim:  To get insight in the principles of semiparametric statistics 
Contents:  In classical statistics models with a (finite dimensional) parameter are studied. These models can be extended to so called semiparametric models by adding infinite dimensional parameters. The simplest example is the extension of the location model, where the distribution is assumed to be normal, to a model where the distribution is still assumed to be symmetric, but otherwise arbitrary. The theory that will be reviewed has been developed during the last fifteen years. This theory will be illustrated by the above mentioned symmetric location model, as well as by the Cox proportional hazards model (applied in Medical Statistics) and the regression model of Engle, Granger, Rice and Weis (Econometrics). 
Literature:  (optional) Bickel, P., Klaassen, C.A.J., Ritov. Y. and J.A. Wellner (1993), Efficient and Adaptive Estimation for Semiparametric Models. Johns Hopkins, Baltimore and London 
Prerequisites:  Measure theoretic probability theory, basic statistics and some functional analysis. 
Title:  Course Analysis of Variance and Design of Experiments 
Lecturers:  dr.ir. E.E.M. van Berkum and ir. R.W.M. Jeurissen. address of Van Berkum: University of Technology HG 9.01 P.O. Box 513 5600 MB Eindhoven tel:0402472903 ( ) 
Time:  spring 1998 
Aim: 
A student who attended the course must be able to

Structure:  The course is given in 9 weeks. In each week 4 lectures of 45 minutes each are given(in dutch). Moreover, there is a tutorial of 2 hours each week. There is an exam of 3 hours. 
Contents: 
The main topics of the course are

Literature: 

Prerequisites:  It is necessary to know the basic principles of statistics (estimation, confidence intervals, hypothesis testing) and to have some knowledge of regression analysis. 
Examination:  It is possible to solve a practical problem in stead of 25% of the exam. 
Title:  Course Mathematical Statistics 2 
Lecturers:  dr. J.H.J. Einmahl () and dr. A. Di Bucchianico (tel:0402472902 () University of Technology Eindhoven HG 9.02 P.O. Box 513 5600 MB Eindhoven. 
Time:  autumn 1997. 
Aim:  Estimation is a very important issue in statistics. In basic statistical courses much attention is paid to estimation of parameters (including confidence intervals). In practice (e.g. statistical quality control) this is very often not enough. One needs to estimate functions of parameters (e.g. quantiles or the probability that a random variable exceeds a certain specified value). The aim of this course is to give an introduction with respect to this kind of topic. Key words are "tolerance intervals" and "density estimation". Moreover this course gives an introduction on "Empirical processes", a modern tool in statistics. The teachers want to give a solid theoretical background for the use of statistics in practice. 
Structure:  The course is given in 9 weeks. In each week 3 lectures of 45 minutes each are given. In these lectures tutorials are included. 
Contents:  In the first two weeks estimation of functions of parameters and tolerance intervals are discussed. In the next 5 weeks an introduction is given on empirical processes. This theory will be applied on the asymptotic distribution of some nonparametric tests and on tolerance intervals. QQ plots will also be discussed. As an illustration of the use of QQ plots among other things tests on normality (e.g. ShapiroWilk) will be treated. In the last two weeks density estimation will be discussed with emphasis on kernel estimators. 
Literature:  A syllabus (in english) will be used. 
Prerequisites:  It is necessary to know the basic principles of statistics (estimation, confidence intervals, hypothesis testing). 
Examination:  There will be an oral exam. 