Ecole d'hiver 2013

3 au 6 février 2013

Sylvain Sardy

Professor Sylvain Sardy (University of Geneva)

Elvezio RONCHETTI (University of Geneva) "ROBUSTNESS"

Peter DIGGLE (Lancaster University), "SPATIAL STATISTICS"

Roger KOENKER (University of Illinois), "QUANTILE REGRESSION"

Andreas RUCKSTUHL (Workshop), Robust Methods in Statistical Data Analysis with R

Professor Elvezio RONCHETTI (University of Geneva) 

Overview

Classical statistics relies largely on parametric models. Typically, assumptions are made on the structural and the stochastic parts of the model and optimal procedures are derived under these assumptions.
Standard examples are least squares estimators in linear models and their extensions, maximum likelihood estimators and the corresponding likelihood-based tests, and GMM techniques in econometrics.

Robust statistics deals with deviations from the stochastic assumptions and their dangers for classical estimators and tests and develops statistical procedures which are still reliable and reasonably efficient in the presence of such deviations. It can be viewed as a statistical theory dealing with approximate parametric models by providing a reasonable compromise between the rigidity of a strict parametric approach and thepotential difficulties of interpretation of a fully nonparametric analysis.

Many classical procedures are well-known for not being robust. These procedures are optimal when the assumed model holds exactly, but they are biased and/or inefficient when small deviations from the model are present. The statistical results obtained from standard classical procedures on real data applications can therefore be misleading.

These lectures will give a brief introduction to robust statistics by reviewing some basic general concepts and tools and by showing how they can be used in data analysis to provide an alternative complementary analysis with additional useful information.

Robust procedures will be discussed for standard models, including linear models, GLM, and multivariate analysis. Some recent developments in more complex models will also be outlined.

Lecture 1

Introduction, motivation
Basic approaches: minimax, infinitesimal approach
Basic tools: statistical functionals, sensitivity curve and influence function, breakdown point 
M-estimators 
Optimal robust estimators

Lecture 2

Robust inference and model selection
High-breakdown estimators
Linear models
GLM and longitudinal models
Multivariate analysis

Lecture 3

Robust Generalized Method of Moments
Indirect inference
Accurate small sample robust inference
Some other recent developments
Main contributions of robust statistics to the development of modern statistics

Professor Peter DIGGLE (Lancaster University) 

Extending Model-Based Geostatistics

In this series of three lectures, I will rst cover model-based geostatistical methods as introduced by Diggle, Moyeed and Tawn (1998) and described at greater length in Diggle and Ribeiro (2007). I will then consider recent work extending the methodology in various ways: allowing for preferential sampling; analysing spatio-temporal data; and the connection between geostatistical and point process methods. Methodological content will be interwoven with applications in the environmental and health sciences, and with demonstrations of one or more R packages.

Lecture 1

In this rst lecture I will give a brief historical introduction to classical geostatistics and explain what is meant by \model-based" geostatistics (Diggle, Moyeed and Tawn, 1998). I will then introduce the linear Gaussian geostatistical model and use this as a framework for discussing the following topics: exploratory analysis; classical and Bayesian likelihood-based inference; spatial prediction; design.

Lecture 2

In this lecture I will brie y consider three extensions to the linear Gaussian model. I will rst dene generalized linear geostatistical models, and describe an application of univariate and bivariate logistic geostatistical models to large-scale disease mapping in Africa.I will then discuss the problem of preferential sampling, which arises when the focus of scientic interest is a latent spatial process fS(x) : x 2 Ag for some planar region A, noisy measurements of S(xi) are available at a nite set of locations xi 2 A, called the sampling design, and the sampling design is stochastically dependent on the process S() Finally, I will consider ways of extending purely spatial geostatistical models to spatiotemporal settings.

Lecture 3

In this lecture I will discuss the connection between point processes and geostatistics, and will argue for a re-denition of geostatistics to include environmentally driven point processes. In particular, I will suggest that the of log-Gaussian Cox process (LGCP) is a direct analogue for spatial point process data of the linear Gaussian model for spatial measurement data. I will discuss likleihood-based methods of inference for LGCP's and describe epidemiological applications of LGCP's in both spatial and spatio-temporal settings.

References

The course gives a personal view of the subject, covering material taken from the following publications. I am pleased to acknowledge the very substantial contributions made by my many collaborators, including but not restricted to those whose names appear below. 
Crainiceanu, C., Diggle, P.J. and Rowlingson, B.S. (2008) Bivariate modelling and rediction of spatial variation in Loa loa prevalence in tropical Africa (with Discussion). Journal of the American Statistical Association, 103, 21{43.

Diggle, P.J. and Lophaven, S. (2006). Bayesian geostatistical design. Scandinavian Journal of Statistics, 33, 55{64.

Diggle, P.J., Menezes, R. and Su, T-L. (2010). Geostatistical analysis under preferential sampling (with Discussion). Applied Statistics, 59, 191{232.

Diggle, P.J., Moraga, P., Rowlingson, B. and Taylor, B. (2013). Spatial and spatio-temporal log-Gaussian Cox processes: methodology and epidemiological applications (in preparation)

Diggle, P.J., Moyeed, R.A. and Tawn, J.A. (1998). Model-based geostatistics (with Discussion). Applied Statistics, 47, 299{350.

Diggle, P.J. and Ribeiro, P.J. (2007). Model-based Geostatistics. New York: Springer.

Diggle, P.J., Thomson, M.C., Christensen, O.F., Rowlingson, B., Obsomer, V., Gardon, J., Wanji, S., Takougang, I., Enyong, P., Kamgno, J., Remme, H., Boussinesq, M. and Molyneux, D.H. (2007). Spatial modelling and prediction of Loa loa risk: decision making under uncertainty. Annals of Tropical Medicine and Parasitology, 101, 499{509.

Rodrigues, A. and Diggle, P.J. (2010). A class of convolution-based models for spatio-temporal processes with non-separable covariance structure. Scandinavian Journal of Statistics, 37,553{567.

Zoure, H., Wanji, S., Noma, M., Amazigo, U., Diggle, P.J., Tekle, A. and Remme, J.H. (2011).The geographic distribution of Loa loa in Africa: results of large-scale implementation of the Rapid Assessment Procedure for Loiasis (RAPLOA). Public Library of Science: Neglected Tropical Diseases, 5, (6): e1210.doi:10.1371/journal.pntd.0001210

Professor Roger KOENKER (University of Illinois)

Quantile regresson extends classical least squares methods for estimating conditional mean functions by oering a variety of methods for estimating conditional quantile functions, thereby enabling the researcher to explore more thoroughly heterogeneous covariate eects. The course will offer a comprehensive introduction to quantile regression methods and brie y survey some recent developments. The primary reference for the course will be my 2005 Econometric Society monograph, but further readings are suggested below in this course outline.
Course lectures will be complemented by a computationally oriented interlude designed to give students some experience with applications of the methods. This session will be conducted in the open-source R language, and will rely on my quantreg package. Thus it would be helpful if students brought laptops equipped with R already installed. R can be freely downloaded for PC/Mac/Linux machines from CRAN: cran.r-project.org. The quantreg package is also available from CRAN, and can be downloaded using the install.packages(``quantreg'') command in its binary form or from source by just clicking on "packages" on the left margin of the CRAN page and following the directions you will find there.

Tentative Topics
(1) The Basics: What, Why and How? Koenker (2005, x1-2),
Koenker and Hallock (2001)
(2) Inference and Quantile Treatment Eects Koenker (2005, x3),
(3) Nonparametric Quantile Regression Koenker (2005, x7), Koenker
(2010),Belloni and Chernozhukov (2009)
(4) Endogoneity and IV Methods Chesher (2003) Chernozhukov
and Hansen (2005) Ma and Koenker (2005)
(5) Censored QR and Survival Analysis Koenker and Geling (2001)
Portnoy (2003) Peng and Huang (2008) Koenker (2008)
(6) Quantile Autoregression Koenker and Xiao (2006)
(7) QR for Longitudinal Data Koenker (2004) Galvao (2009)
(8) Risk Assessment and Choquet Portfolios Bassett, Koenker, and
Kordas (2004)
(9) Quantile Regression Computation: From the Inside and Out-
side Koenker (2005, x6)

References

Bassett, G., R. Koenker, and G. Kordas (2004): \Pessimistic Portfolio Allocation and Choquet Expected Utility," J. of Financial Econometrics, 2, 477{92.
Belloni, A., and V. Chernozhukov (2009): \L1-Penalized Quantile Regression in High-Dimensional Sparse Models," forthcoming Annals of Statistics.
Chernozhukov, V., and C. Hansen (2005): \An IV Model of Quantile Treatment Eects," Econometrica, 73(1), 245{261.
Chesher, A. (2003): \Identication in Nonseparable Models," Econometrica, 71,1405{1441.
Galvao, A. (2009): \Quantile Regression for Dynamic Panel Data with Fixed Eects," forthcoming, J. of Econometrics.
Koenker, R. (2004): \Quantile Regression for Longitudinal Data," Journal of Multivariate Analysis, 91, 74{89.
(2005): Quantile Regression. Cambridge.
(2008): \Censored Quantile Regression Redux," J. of Statistical Software,
27(6), 1{24.
(2010): \Additive Models for Quantile Regression: Model Selection and
Condence Bandaids," forthcoming, Brazilian J. of Statistics.
Koenker, R., and O. Geling (2001): \Reappraising Med y Longevity: A quantile regression survival analysis," J. of Am. Stat. Assoc., 96, 458{468.
Koenker, R., and K. Hallock (2001): \Quantile Regression," J. of Economic Perspectives, 15, 143{156.
Koenker, R., and Z. Xiao (2006): \Quantile Autoregression, with discussion and rejoinder," J. of Am. Stat. Assoc., 96, 980{1006.
Ma, L., and R. Koenker (2005): \Quantile Regression for Recursive Structural
Models," J. of Econometrics, 134, 471{506.
Peng, L., and Y. Huang (2008): \Survival Analysis with Quantile Regression
Models," J. of Am. Stat. Assoc., 103(482), 637{649.
Portnoy, S. (2003): \Censored Quantile Regression," J. of Am. Stat. Assoc., 98,
1001{1012.

Professor Ruckstuhl Andreas (Workshop)

Models consisting of a structural and a stochastic part are often used for analysing data. As these statistical models still contain unknown parameters, inferential procedures must be derived. Based on the assumption that the observed data are realisations of such a statistical model, optimal procedures are derivedHowever, it is generally understood that such models are simplifications of reality and that their validity is at best approximative. In contrast to classicalinferential methods robust methods are less sensitive to deviations from the assumptions in the model.

Over the last fifty years robust fitting and inferential methods have been derived for many statistical models. Many of them are implemented now in R. These lectures will introduce to statistical data analysis with robust methods mainly using the R package robustbase.

Lecture 1 (Robust Regression using lmrob() and rlm())

* M- and GM-estimation

    * Case study using air quality data

    * Case study using data from molecular spectroscopy

* MM-estimation

    * Case study using financial data

* Robust inference using anova(); i.e. anova.lmrob()

Lecture 2 (GLM and multivariate analysis)

* Robust inference with GLM using glmrob() and anova()

* Robust estimation of covariance matrices

* Linear discriminant analysis

* An application of robust fitting methods beyond theory

PROGRAMME

Les Diablerets

 Eurotel Victoria
 1865 Les Diablerets (VD) 

http://www.eurotel-victoria.ch/diablerets/

Accès aux Diablerets EN VOITURE

Autoroute A9, direction Grand St-Bernard, sortie Aigle. Puis la route Aigle - Les Diablerets - Col du Pillon (20km).  EN AVION
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 International
 TGV Paris - Lausanne. En hiver, TGV des Neiges Paris - Lausanne - Aigle. 
 Suisse
 Train schedule  : From: Geneve airport, To: Les Diablerets, gare.  Trains directs jusqu'à Aigle. Ensuite train de montagne A.S.D (Aigle - Sépey - Diablerets)
 Durée des trajets: Lausanne - Aigle (30 minutes), Aigle - Les Diablerets (50 minutes).  Visa pour la Suisse (Visa for Switzerland) Météo en suisse  (Quel temps fait-il dans notre pays ? - Weather in Switzerland ?)

Doctorant CUSO chambre double: 150 CHF Doctorant CUSO chambre simple: 300 CHF

Post-doctorant CUSO chambre double: 250 CHF Post-doctorant CUSO chambre simple: 400 CHF

Professeur CUSO chambre double: 350 CHF Professeur CUSO chambre simple: 500 CHF

Non CUSO universitaire chambre double: 600 CHF Non CUSO universitaire chambre simple: 750 

Non CUSO privé chambre double: 1100 CHF Non CUSO privé chambre simple: 1250 CHF

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