École d’été

10 - 13 septembre 2014

Valérie Chavez Demoulin (Université de Lausanne) Mervat Cluzeau (Université de Genève)

Richard Samworth : University of Cambridge, Title : Modern high-dimensional statistics
 Thomas Mikosch: University of Copenhagen, Title : Heavy tailed time series
 JNK Rao : Carleton University
Verity Elston : Workshop : « Skills in turbo-drive,  tools to help you through the doctorate and for the future (CUSO Skills Programme)”

Professor Richard Samworth : University of Cambridge

Title: High-dimensional statistical inference

Abstract: In the 20th century, data sets tended to be fairly small, and statistical models tended to involve relatively few parameters toestimate. These days, however, modern technology allows us to collect and store data sets on previously unimaginable scales in diverse fields such as genetics, medical imaging and astronomy. Moreover, we are often faced with situations where the model dimension exceeds the sample size. I will describe some of the key methodological and theoeretical statistical ideas that have been developed over the last 15 years or so to handle such situations.

 Lecture 1: Brief review of the standard linear model, illustrated with an example. Ridge regression. Traditional model selection approaches: best subset selection, AIC, BIC, forward selection. Definition of the Lasso, illustrated with an example.

Lecture 2: Geometric intuition and theoretical properties of the Lasso.
Coordinate descent. Extensions to other models/penalties.

Lecture 3: Stability selection and Complementary Pairs Stability
Selection. Multiple testing, Bonferroni correction, false discovery rate, the Benjamini--Hochberg procedure.

 References:
Buehlmann, P. and van de Geer, S. (2011) Statistics for High-Dimensional Ferreira, J. A. and Zwinderman, A. H. (2006) On the Benjamini--Hochberg method, Ann. Statist., 34, 1827--1849. Hastie, T., Tibshirani, R. and Friedman, J. (2009) The Elements of Statistical Learning, Springer.
Meinshausen, N. and Buehlmann, P. (2010) Stability Selection (with discussion), J. Roy. Statist. Soc., Ser. B 72, 417-473.
Shah, R. D. and Samworth, R. J. (2013), Variable selection with error control: Another look at Stability Selection, J. Roy. Statist. Soc., Ser.B, 75, 55-80.

 SLIDES

Professor Thomas Mikosch : University of Copenhagen

Title: Heavy Tail Phenomena

Course description: In this course we study the interplay between heavy tails of distributions and processes, and their dependence structure. A useful notion for describing heavy tails is regular variation. Early on, this notion was propagated in Sid Resnick's (1987) monograph. Since then, regular variation has become a major probabilistic tool for describing heavy tail
phenomena; see Resnick (2007) for a recent summary of the theory and applications.
Regular variation describes power law behavior in the tails of random vectors and stochastic processes. It is a natural modeling condition: Regular variation is the maximum domain condition for anely transformed maxima of a sequence of iid random vectors and it is the domain of attraction condition for anely transformed partial sums of a sequence of iid random
vectors with in nite variance.
The notion of regular variation is a exible tool for describing both spatiotemporal extremal dependence and heavy tails. Its multivariate version can be applied to time series and stochastic processes. For example, max-stable and sum-stable processes and random elds have regularly varying nite-dimensional distributions. Large classes of nancial time series models such as GARCH, stochastic volatility and related models are regularly varying; see Davis and Mikosch (2009a,b). There is strong evidence that quantities such as le sizes, transmission durations and throughput rates in telecommunications networks (such as the Internet) have regularly varying distributions; see Resnick (2007). (Re)insurance data are also well modeled by
distributions with power law tails.
The aim of this course is to give a gentle introduction to the eld of heavy tail phenomena. Theory and applications are centered around the notion of regular variation. We discuss how regular variation enters applied probability models and how functions of regularly varying time series and stochasticprocesses are in uenced by heavy tail components. Special attention will be given to large deviation probabilities for sums of serially dependent random vectors. We touch on the statistical problem of measuring serial extremal dependence. A major tool will be the extremogram introduced in Davis and Mikosch (2009c). It is an analog of the autocorrelation function tailored for serial extremal dependence. In view of this analogy, one can also conduct Fourier analyses of serially dependent extremal events.
Short description of the 3 1.5 hour lectures.
1. Lecture We look at some data from nance, insurance and telecommunications and discuss how we can measure the heaviness of the tails for univariate and multivariate data. We are also interested in measuring extremal dependence in space and time. We discuss tools
such as the tail dependence coecient, the extremal index and the extremogram.
2. Lecture We introduce the notion of regular variation. This means power law behavior of the tails in univariate and multivariate situations. We consider typical examples such as the autoregressive and moving average processes with regularly varying innovations, but also
non-linear processes such as the GARCH process. We explain how regular variation can be applied to derive asymptotic results for the extremes, sums, ruin and other functionals acting on dependent heavy-tailed sequences.
3. Lecture We consider applications of regular variation calculus to problems of large deviations for sums of dependent data, to max-stable processes and elds and to heavy-tailed sample covariance matrices.
References.
1. Davis, R.A. and Mikosch, T. (2009a) Extreme value theory for
GARCH processes. In: Andersen, T.G., Davis, R.A., Kreiss,
J.-P. and Mikosch, T. (2009) Handbook of Financial Time Series.
Springer, Berlin, pp. 187{199.
2. Davis, R.A. and Mikosch, T. (2009b) Extremes of stochastic
volatility processes. In: Andersen, T.G., Davis, R.A., Kreiss,
J.-P. and Mikosch, T. (2009) Handbook of Financial Time Series.
Springer, Berlin, pp. 355{364.
3. Davis, R.A. and Mikosch, T. (2009c) The extremogram: a cor-
relogram for extreme events. Bernoulli 15, 977{1009.
4. Resnick, S.I. (1987) Extreme Values, Regular Variation, and Point
Processes. Springer, New York.
5. Resnick, S.I. (2007) Heavy-Tail Phenomena. Probabilistic and Sta-
tistical Modeling. Springer, New York.

 SLIDES

Professor JNK Rao : Carleton University-Ottawa Canada         

Title: Small Area Estimation: Methods and Applications

Course Outline : Small area estimation is a topic of current interest because of growing demand for reliable small area statistics. This short course will provide an introduction to theory and methods of small area estimation (SAE).  Basic introduction to traditional sample survey theory and standard linear regression models will be provided before proceedings to SAE methods that require linear fixed and random effects models and extensions. Introduction to Bayesian methods will also be needed.

 1. Traditional sample survey theory

Contents will include (a) finite population parameters of interest (b) sampling frames (c) sampling methods (d) sampling weights and (e) estimation of parameters and variance estimation.

2. Traditional SAE

Contents will include (a) planned and unplanned domains, (b) design issues, (c) synthetic and composite estimation, (d) MSE estimation.

3. Basic area level models

Topics to be covered will include (a) Fay-Herriot model, (b) empirical best linear unbiased prediction (EBLUP), (c) methods for estimating MSE including linearization, jackknife and bootstrap, (d) benchmarking to direct aggregate estimators, (e) model selection and validation and (f) applications to real data.

4. Basic unit level models

Topics to be covered include (a) nested error linear regression model, (b) EBLUP and MSE estimation, (c) model selection and validation, (d) pseudo-EBLUP using survey weights.

5. Hierarchical Bayes (HB) approach

Topics to be covered will include (a) posterior mean and variance, (b) application of HB to basic area level model, (c) Bayesian methods for model validation.

6. Empirical best/Bayes (EB) estimation

Topics to be covered will include (a) EB estimation for complex parameters, (b) application to estimation of poverty indicators and comparison with the World Bank simulated census method, (d) application to Spanish Income and Living Conditions dat.

7. Conclusions and recommendations

SLIDES

Verity Elston : Workshop

Title: « Skills in turbo-drive
Tools to help you through the doctorate and for the future (CUSO Skills Programme)”

<link file:7013 download file>SLIDES

Programme :

HOTEL MERCURE Bristol Leukerbad Badehotel Bristol AG,Rathausstrasse 51 3954 Leukerbad

Mercure Bristol Leukerbad / Loeche les Bains

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En voiture : depuis Leuk Susten, prendre la direction de Loèche-les-Bains (Leukerbad) sur 16 km. Arrivé à Loèche-les-Bains, tourner à droite au premier rond-point, puis à gauche 100m plus loin. Vous êtes arrivé à l'hôtel Mercure Bristol. En train : àLeuk Susten, prendre le car pour Loèche-les-Bains. La navette de l'hôtel gratuite viendra vous chercher à la gare de Loèche-les-Bains si vous leur communiquez votre heure d'arrivée.

Doctorant CUSO chambre double ou quadruple : CHF 150
Doctorant CUSO chambre simple: CHF 250 Post-doctorant CUSO chambre double : CHF 220
Post-doctorant CUSO chambre simple: CHF 320 Professeur CUSO chambre double : CHF 285
Professeur CUSO chambre simple: CHF 385 Non CUSO universitaire chambre double : CHF 450
Non CUSO universitaire chambre simple: CHF 550 Non CUSO privé chambre double : 785 CHF
Non CUSO privé chambre simple: 885 CHF

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