Journal of Statistical Theory and Applications

Volume 12, Issue 3, September 2013, Pages 288 - 305

Quantile regression in high-dimension with breaking

Authors
Gabriela Ciuperca
Corresponding Author
Gabriela Ciuperca
Available Online 1 September 2013.
DOI
https://doi.org/10.2991/jsta.2013.12.3.6How to use a DOI?
Keywords
change-points; high-dimension; oracle properties; SCAD; LASSO-type estimators
Abstract
The paper considers a linear regression model in high-dimension for which the predictive variables can change the influence on the response variable at unknown times (called change-points). Moreover, the particular case of the heavy-tailed errors is considered. In this case, least square method with LASSO or adaptive LASSO penalty can not be used since the theoretical assumptions do not occur or the estimators are not robust. Then, the quantile model with SCAD penalty or median regression with LASSO-type penalty allows, in the same time, to estimate the parameters on every segment and eliminate the irrelevant variables. We show that, for the two penalized estimation methods, the oracle properties is not affected by the change-point estimation. Convergence rates of the estimators for the change-points and for the regression parameters, by the two methods are found. Monte-Carlo simulations illustrate the performance of the methods.
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Journal
Journal of Statistical Theory and Applications
Volume-Issue
12 - 3
Pages
288 - 305
Publication Date
2013/09
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.2013.12.3.6How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Gabriela Ciuperca
PY  - 2013
DA  - 2013/09
TI  - Quantile regression in high-dimension with breaking
JO  - Journal of Statistical Theory and Applications
SP  - 288
EP  - 305
VL  - 12
IS  - 3
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2013.12.3.6
DO  - https://doi.org/10.2991/jsta.2013.12.3.6
ID  - Ciuperca2013
ER  -