Censored quantile regression processes under dependence and penalization
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Date
2012-08-28
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Abstract
We consider quantile regression processes from censored data under dependent data
structures and derive a uniform Bahadur representation for those processes. We also
consider cases where the dimension of the parameter in the quantile regression model
is large. It is demonstrated that traditional penalization methods such as the adaptive
lasso yield sub-optimal rates if the coe fficients of the quantile regression cross zero. New
penalization techniques are introduced which are able to deal with speci c problems
of censored data and yield estimates with an optimal rate. In contrast to most of
the literature, the asymptotic analysis does not require the assumption of independent
observations, but is based on rather weak assumptions, which are satis ed for many
kinds of dependent data.
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Keywords
Bahadur representation, censored data, dependent data, quantile regression, variable selection, weak convergence