## Electronic Journal of Statistics

### Censored quantile regression processes under dependence and penalization

#### 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 coefficients of the quantile regression cross zero. New penalization techniques are introduced which are able to deal with specific 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 satisfied for many kinds of dependent data.

#### Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 2405-2447.

Dates
First available in Project Euclid: 14 November 2014

https://projecteuclid.org/euclid.ejs/1415976172

Digital Object Identifier
doi:10.1214/14-EJS54

Mathematical Reviews number (MathSciNet)
MR3278338

Zentralblatt MATH identifier
1349.62488

Subjects
Primary: 62N02: Estimation

#### Citation

Volgushev, Stanislav; Wagener, Jens; Dette, Holger. Censored quantile regression processes under dependence and penalization. Electron. J. Statist. 8 (2014), no. 2, 2405--2447. doi:10.1214/14-EJS54. https://projecteuclid.org/euclid.ejs/1415976172

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