[Statlist] RESEARCH SEMINAR IN STATISTICS - UNIVERSITY OF GENEVA

[Eva Cantoni]

RESEARCH SEMINAR IN STATISTICS - UNIVERSITY OF GENEVA

Organisers :
E. Cantoni - E. Ronchetti - S. Sperlich - M-P. Victoria-Feser


Friday February 28th, 2014
at 11h15
Room M 5220, Uni Mail (40, bd du Pont-d'Arve, Genève)

Prof. Jonathan EL METHNI
Université de Genève

«Nonparametric estimation of extreme risk measures from conditional 
heavy-tailed distributions»

Abstract:
In this work we introduce and estimate a new risk measure, the so-called 
Conditional Tail Moment. It is defined as the moment of order a>0 of the 
loss distribution above the quantile of order p belonging to (0,1) of 
the survival function. Estimating the Conditional Tail Moment permits to 
estimate all risk measures based on conditional moments such as the 
Value-at-Risk, the Conditional Tail Expectation, the Conditional 
Value-at-Risk, the Conditional Tail Variance or the Conditional Tail 
Skewness. Here, we focus on the estimation of these risk measures in 
case of extreme losses i.e. when p converges to 0 when the size of the 
sample increases. It is moreover assumed that the loss distribution is 
heavy-tailed and depends on a covariate. The estimation method thus 
combines nonparametric kernel methods with extreme-value statistics. The 
asymptotic distribution of the estimators is established and their 
finite sample behavior is illustrated both on simulated data and on a 
real data set of daily rainfalls in the Cévennes-Vivarais region (south 
of France). In this work we introduce and estimate a new risk measure, 
the so-called Conditional Tail Moment. It is defined as the moment of 
order a>0 of the loss distribution above the quantile of order p 
belonging to (0,1) of the survival function. Estimating the Conditional 
Tail Moment permits to estimate all risk measures based on conditional 
moments such as the Value-at-Risk, the Conditional Tail Expectation, the 
Conditional Value-at-Risk, the Conditional Tail Variance or the 
Conditional Tail Skewness. Here, we focus on the estimation of these 
risk measures in case of extreme losses i.e. when p converges to 0 when 
the size of the sample increases. It is moreover assumed that the loss 
distribution is heavy-tailed and depends on a covariate. The estimation 
method thus combines nonparametric kernel methods with extreme-value 
statistics. The asymptotic distribution of the estimators is established 
and their finite sample behavior is illustrated both on simulated data 
and on a real data set of daily rainfalls in the Cévennes-Vivarais 
region (south of France).

Keywords : Extreme-value statistics, Nonparametric statistics, Risk 
measure, Heavy-tailed distributions.


http://www.stat-center.unige.ch/ResSem.html

-- 
Prof. Eva Cantoni
Research Center for Statistics and
      Geneva School of Economics and Management
University of Geneva, Bd du Pont d'Arve 40, CH-1211 Genève 4
http://www.unige.ch/ses/dsec/staff/faculty/Cantoni-Eva.html