Abstract
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  7 Dec 2016 
Place of Publication  Tilburg 
Publisher  
Print ISBNs  9789056684952 
Publication status  Published  2016 
Fingerprint
Cite this
}
A large deviations approach to the statistics of extreme events. / de Valk, Cees.
Tilburg : CentER, Center for Economic Research, 2016. 133 p.Research output: Thesis › Doctoral Thesis › Scientific
TY  THES
T1  A large deviations approach to the statistics of extreme events
AU  de Valk, Cees
PY  2016
Y1  2016
N2  A large deviations approach to the statistics of extreme events addresses the statistical analysis of extreme events with very low probabilities: given a random sample of data of size n, the probability is much smaller than 1/n. In particular, it takes a close look at the regularity assumptions on the tail of the (univariate or multivariate) distribution function. The classical assumptions, cast in the form of limits of ratios of probabilities of extreme events, are not directly applicable in this setting. Therefore, additional assumptions are commonly imposed. Because these may be very restrictive, this thesis proposes an alternative regularity assumption, taking the form of asymptotic bounds on ratios of logarithms of probabilities of extreme events, i.e., a large deviation principle (LDP). In the univariate case, this tail LDP is equivalent to the logGeneralised Weibull (logGW) tail limit, which generalises the Weibull tail limit and the classical Pareto tail limit, amongst others. Its application to the estimation of high quantiles is discussed. In the multivariate case, the tail LDP implies marginal logGW tail limits together with a standardised tail LDP describing tail dependence. Its application to the estimation of very low probabilities of multivariate extreme events is discussed, and a connection is established to hidden regular variation (residual tail dependence) and similar models.
AB  A large deviations approach to the statistics of extreme events addresses the statistical analysis of extreme events with very low probabilities: given a random sample of data of size n, the probability is much smaller than 1/n. In particular, it takes a close look at the regularity assumptions on the tail of the (univariate or multivariate) distribution function. The classical assumptions, cast in the form of limits of ratios of probabilities of extreme events, are not directly applicable in this setting. Therefore, additional assumptions are commonly imposed. Because these may be very restrictive, this thesis proposes an alternative regularity assumption, taking the form of asymptotic bounds on ratios of logarithms of probabilities of extreme events, i.e., a large deviation principle (LDP). In the univariate case, this tail LDP is equivalent to the logGeneralised Weibull (logGW) tail limit, which generalises the Weibull tail limit and the classical Pareto tail limit, amongst others. Its application to the estimation of high quantiles is discussed. In the multivariate case, the tail LDP implies marginal logGW tail limits together with a standardised tail LDP describing tail dependence. Its application to the estimation of very low probabilities of multivariate extreme events is discussed, and a connection is established to hidden regular variation (residual tail dependence) and similar models.
M3  Doctoral Thesis
SN  9789056684952
T3  CentER Dissertation Series
PB  CentER, Center for Economic Research
CY  Tilburg
ER 