Mathematics – Statistics Theory
Scientific paper
2008-06-15
Extremes 15, 1 (2012) 1-34
Mathematics
Statistics Theory
32 pages, 5 figure
Scientific paper
10.1007/s10687-010-0122-6
Let $(X,Y)$ be a bivariate random vector. The estimation of a probability of the form $P(Y\leq y \mid X >t) $ is challenging when $t$ is large, and a fruitful approach consists in studying, if it exists, the limiting conditional distribution of the random vector $(X,Y)$, suitably normalized, given that $X$ is large. There already exists a wide literature on bivariate models for which this limiting distribution exists. In this paper, a statistical analysis of this problem is done. Estimators of the limiting distribution (which is assumed to exist) and the normalizing functions are provided, as well as an estimator of the conditional quantile function when the conditioning event is extreme. Consistency of the estimators is proved and a functional central limit theorem for the estimator of the limiting distribution is obtained. The small sample behavior of the estimator of the conditional quantile function is illustrated through simulations.
Fougères Anne-Laure
Soulier Philippe
No associations
LandOfFree
Estimation of conditional laws given an extreme component does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Estimation of conditional laws given an extreme component, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Estimation of conditional laws given an extreme component will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-258271