In this paper, we propose two types of estimator (one of histogram type, the other a kernel estimate) of the quantile density (or sparsity) function α\mapsto [f(F-1(α ))]-1 associated with the innovation density f of an autoregressive model of order p. Our estimators are based on autoregression quantiles. Contrary to more classical estimators based on estimated residuals, they are autoregression-invariant and scale-equivariant. Their asymptotic behaviour is derived from a uniform Bahadur representation for autoregression quantiles - a result of independent interest. Simulations are carried out to illustrate their performance.
Publié le : 2002-04-14
Classification:
autoregression,
autoregression quantiles,
Bahadur-Kiefer representation,
histogram estimator,
kernel estimator,
quantile density function,
sparsity function
@article{1078866870,
author = {El Bantli, Faouzi and Hallin, Marc},
title = {Estimation of the innovation quantile density function of an AR(p) process based on autoregression quantiles},
journal = {Bernoulli},
volume = {8},
number = {2},
year = {2002},
pages = { 255-274},
language = {en},
url = {http://dml.mathdoc.fr/item/1078866870}
}
El Bantli, Faouzi; Hallin, Marc. Estimation of the innovation quantile density function of an AR(p) process based on autoregression quantiles. Bernoulli, Tome 8 (2002) no. 2, pp. 255-274. http://gdmltest.u-ga.fr/item/1078866870/