[Statlist] talks on statistics

[Christina Kuenzli]

              ETH and University of Zurich 

                           Proff. 
         A.D. Barbour - P. Buehlmann - F. Hampel 
              H.R. Kuensch - S. van de Geer

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       We are glad to announce the following talks
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     Friday, Mai 25th, 2007  15.15h  LEO C 6
 
     Empirical portfolio selection
     Laszlo Gyoerfi Budapest University

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     Friday, June 1st, 2007          

     
     15.15 - 16.00         LEO C 6
     Case series models for censoring eventsx
     Mounia Hocine and Paddy Farrington
     Departement of Statistics, The Open University, UK

A case series is a sample of cases, that is, individuals who have
  experienced an event of interest. Inferences on the association between
  an exposure and an outcome event can be derived from case series data
  using a variety of methods, one of which is the self-controlled case
  series method, which is the topic of this talk. 

The case series model will be reviewed briefly. The method is particularly
useful for evaluating the association between a transient exposure and an
acute event. However, a key assumption is that the occurrence of exposures
must not be affected by preceding events. This assumption fails for events
that censor subsequent exposures. 

An extension of the case series model, which is valid for censoring events,
will be described. This extension is based on a set of unbiased estimating
equations, derived using a Horvitz-Thompson-like estimator. The efficiency
of the new method will be described analytically in simple cases, and
simulations to illustrate its performance will be presented.  

In realistic scenarios, obtaining point and sandwich variance estimates
directly from the estimating equations can be cumbersome. A simpler
procedure will be described which can be implemented in standard
software. With this approach interval estimates are obtained by
bootstrapping.  

An application to data on oral polio vaccine and intussusception will be
presented  


     16.15 - 17.00         LEO C 6
     Estimating unbounded densities with L_2-loss
     Lucien Birge
     Universite Paris VI, France

Many papers that deal with estimation of a density s \in L_2([0, 1]) from n
i.i.d. observations with a risk being the expectation of the squared 
L_2-distance use (implicitly or not) the additional assumption that s also
belongs to L_infty and typical risk bounds depend on the L_infty-norm of
s. This is readily visible for histograms based on non-regular
partitions. Some counterexamples and lower bound results show that it
partly unavoidable. This is due to the distortion between the Hellinger
and L_2- distances. It is well-known from Le Cam that it is impossible
to distinguish between two densities at a Hellinger distance cn^¡Ý 1/2 with
a small c. But the relations 
 
h^2(f, g) = \frac{1}{2} \int (\sqrt{f} - \sqrt{g})^2 =  \frac{1}{2} \int
    \frac{(f-g)^2}{(\sqrt{f} + \sqrt{g})^2},  | f - g |_2^2
    = \int (f - g)^2. 

indicate that | f - g |_2  may be substantially larger than h(f, g) when  |
f - g |_infty is large, in which case it may be impossible to distinguish
between f and g although  | f - g |_2  is much larger than n^-1/2.

Our purpose is to develop specific tools to estimate densities that do not
belong to L_1. We shall in particular consider the problems of model
selection and aggregation of preliminary estimators, with applications to
the selection of partitions for histograms. The tools are extensions of
those developed in Birge (2006), i.e. arguments based on metric dimensions
and testing between balls, with specific modifications due to the fact that
the difficulty of testing between two L_2-balls is not only a function of
the distance between the balls (as is the case with the Hellinger
distance). 

BIRGE, L. (2006). Model selection via testing : an alternative to
(penalized) maximum likelihood estimators. Ann. Inst. Henri Poincare,
Probab. et Statist. 42, 273-325.

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________________________________________________________
Christina Kuenzli            <kuenzli using stat.math.ethz.ch>
Seminar fuer Statistik      
Leonhardstr. 27,  LEO D11      phone: +41 (0)44 632 3438         
ETH-Zentrum,                   fax  : +41 (0)44 632 1228 
CH-8092 Zurich, Switzerland        http://stat.ethz.ch/~