Volume 12, Issue 3, September 2013, Pages 288 - 305
Quantile regression in high-dimension with breaking
Received 18 February 2013, Accepted 21 July 2013, Available Online 1 September 2013.
- https://doi.org/10.2991/jsta.2013.12.3.6How to use a DOI?
- change-points; high-dimension; oracle properties; SCAD; LASSO-type estimators
- 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.
- 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 -