École d’été

4-7 septembre 2016

Mme Valérie Chavez, UNIL (Présidente) Mme Mervat Cluzeau, UNIGE (coordinatrice)

Professeur Davy Paindaveine, Université libre de Bruxelles
Professeur Raymond Carroll, Texas A&M University
Docteur Shaun Seaman, MRC Biostatistics Unit

Professor Davy Paindaveine

(Université libre de Bruxelles)

Slides

Title : From statistical depth to multivariate quantiles

Abstract

 Statistical depth aims at measuring centrality of any given location in the d-dimensional Euclidean space with respect to probability distributions over that space. For empirical distributions, depth provides (i) a deepest point, that usually can be seen as a multivariate median, and (ii) a center-outward ordering of the observations. Depth may therefore be considered as a concept of multivariate ranks. In this short course, we will introduce the main concepts of depth, including Tukey's halfspace depth and Liu's simplicial depth. We will present some well-known properties and discuss Serfling's axiomatic approach. We will then briefly describe some inferential applications of depth. We further plan to discuss local extensions of the concept and, if time permits, will describe how depth can be modified to cope with regression and functional data. The strong relation between depth and multivariate quantiles will be examined, and we plan to show how this relation can be used to define appropriate multiple-output regression quantiles.

Doctor Shaun Seaman

(MRC Biotatistics Unit)

Slides

Title : The Analysis of Incomplete Data

Abstract

The task of analysing a data set is often complicated in practice by those data being incomplete, that is, some of the data that were planned to be collected are missing. There are numerous causes for such missing data: experiments or measurement devices can fail; records may be lost; people refuse to participate in surveys or they participate but then decline to answer certain questions; individuals may drop out of a cohort study. The aim of this course is to provide a toolkit of statistical methods for analysing incomplete data. There will be an emphasis throughout the course on the assumptions under which the various methods studied provide valid inference, and examples of analyses using these methods will be given.In the first lecture, I shall begin by discussing the consequences of data being incomplete: estimates can be biased, statistical efficiency lost, and uncertainty un- derestimated. We shall then look at ad-hoc statistical methods for dealing with incomplete data. Such methods include restricting the analysis to study units with complete data (the so-called 'complete-case analysis') or replacing the missing val- ues in a variable by the observed mean of this variable ('mean imputation'). Then I shall introduce the concept of a missingness mechanism and describe Rubin's traditional classification of mechanisms as either missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR). The MAR assumption, in particular, is an important assumption; it means that the data that are observed are, in a specific sense, representative of the data that are missing. Many advanced methods for handling missing data assume that data are MAR. Such methods will then be introduced. These include multiple imputation (MI), inverse probability weighting (IPW), and observed-data maximum likelihood.In the second lecture, I shall discuss these more advanced methods in detail. MI, which is a very popular approach, involves replacing the missing values with values that are 'consistent' with the observed data and doing this multiple times in a way that enables the uncertainty in these missing values to be reflected. Various flavours of MI will be described. IPW involves weighting up the observed data in such a way that they represent both themselves and the missing data. Although arguably not as flexible as MI, IPW can be a useful alternative in some situations, and these will be highlighted. Observed-data maximum likelihood and the related Bayesian approach will also be covered.
In the third lecture, I shall turn to some more advanced topics in incomplete- data methodology. We shall look at the handling of multi-level data, such as data arising from a study of school pupils who are nested within classes, which are themselves nested within schools. Methods that combine imputation and IPW will be discussed. These include the recently developed 'doubly robust' methods. Most methods for analysing incomplete data assume a MAR missingness mechanism. Often, however, one might suspect that the true mechanism is MNAR. So, we shall examine some methods that have been developed to handle MNAR data or to examine the sensitivity of results to a violation of the MAR assumption.

Professor Raymond j. Carroll

(Texas A&M University)

Slides

Title : Measurement Error Modeling: Statistical Analysis When Predictors/Responses Cannot Be Ascertained Without Uncertainty

Abstract

 Measurement error modeling is a short-cut name for statistical analysis when important variables, predictors and/or responses cannot be ascertained (measured) without uncertainty. There is a large literature in this field with applications in economics, biostatistics (nutrition, physical activity, radiation epidemiology, genetic epidemiology and others), political science, etc. The literature tends to split into cases where the not completely measured variable is continuous and when it is discrete (especially binary). The field ranges from highly theoretical to very application-oriented.I will review some of the larger themes in the area, and present the basic theory. The field is too vast to survey everything, so I will then discuss recent research topics in the area, with some focus on my own work.

PROGRAMME

Eurotel Victoria VILLARS

Plan

Doctorant CUSO chambre double : CHF 200
Doctorant CUSO chambre simple: CHF 300
Post-doctorant CUSO chambre double : CHF 250
Post-doctorant CUSO chambre simple: CHF 350
Professeur CUSO chambre double : CHF 300
Professeur CUSO chambre simple: CHF 400
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

Merci de bien indiquer si chambre Simple ou Double dans Commentaire

Versement sur compte postal
Ou sur compte bancaire

CCP 12-1873-8
Neuchâtel
BIC : POFICHBEXXX
IBAN : CH0509000000120018738

 
Bank: UBS SA, CH - 1211 Geneve 2
BIC : UBSWCHZH80A
IBAN : CH37 0024 0240 4723 2800 L (owner: Conférence universitaire de Suisse occidentale, Neuchâtel)
 

65