摘要：In many areas of application, a typical requirement is to estimate a high quantile
1.p of probability 1.p, a value, high enough, so that the chance of an exceedance
of that value is equal to p, small. The semi-parametric estimation of high quantiles
depends not only on the estimation of the tail index , the primary parameter of
extreme events, but also on an adequate estimation of a scale first order parameter.
The great majority of semi-parametric quantile estimators, in the literature, do not
enjoy the adequate behaviour, in the sense that they do not suffer the appropriate
linear shift in the presence of linear transformations of the data. Recently, and for
heavy tails ( > 0), a new class of quantile estimators was introduced with such a
behaviour. They were named PORT-quantile estimators, with PORT standing for
peaks over random threshold. In this paper, also for heavy tails, we introduce a new
class of PORT-quantile estimators with the above mentioned behaviour, using the
PORT methodology and incorporating Hill and moment PORT-classes of tail index
estimators in one of the most recent classes of quantile estimators suggested in the
literature. Under convenient restrictions on the underlying model, these classes of
estimators are consistent and asymptotically normal for adequate k, the number of
top order statistics used in the semi-parametric estimation of 1.p.
关键词：statistics of extremes; heavy tails; high quantiles; semi-parametric estimation; PORT
methodology; asymptotic behaviour.
