TY - JOUR
T1 - Estimation of high conditional quantiles using the Hill estimator of the tail index
AU - He, Fengyang
AU - Cheng, Yebin
AU - Tong, Tiejun
N1 - Funding Information:
Yebin Cheng’s research was supported in part by the National Natural Science Foundation of China Grant (No. 11271241 ). Tiejun Tong’s research was supported in part by the Hong Kong Baptist University FRG grants FRG1/14-15/044 , FRG2/14-15/084 , and FRG2/15-16/019 . The authors thank the editor and the associate editor for their constructive comments that led to a substantial improvement of the paper.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - To implement the extremal quantile regression, one needs to have an accurate estimate of the tail index that is involved in the limit distributions of extremal regression quantiles. However, the existing quantile estimation methods are often unstable owing to data sparsity in the tails. In this paper, we propose the Hill estimator for the tail index based on regression quantiles, and construct a new estimator for high conditional quantiles through an extrapolation of the intermediate regression quantiles. In both theory and simulation, we demonstrate that the proposed estimators are more efficient than those based on the refined Pickands estimator of the tail index. The applicability of the new method is also illustrated on the Occidental Petroleum daily stock return data.
AB - To implement the extremal quantile regression, one needs to have an accurate estimate of the tail index that is involved in the limit distributions of extremal regression quantiles. However, the existing quantile estimation methods are often unstable owing to data sparsity in the tails. In this paper, we propose the Hill estimator for the tail index based on regression quantiles, and construct a new estimator for high conditional quantiles through an extrapolation of the intermediate regression quantiles. In both theory and simulation, we demonstrate that the proposed estimators are more efficient than those based on the refined Pickands estimator of the tail index. The applicability of the new method is also illustrated on the Occidental Petroleum daily stock return data.
KW - Extreme value theory
KW - High conditional quantiles
KW - Hill estimator
KW - Pickands estimator
KW - Quantile regression
KW - Tail index
UR - http://www.scopus.com/inward/record.url?scp=84964689371&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2016.03.003
DO - 10.1016/j.jspi.2016.03.003
M3 - Journal article
AN - SCOPUS:84964689371
SN - 0378-3758
VL - 176
SP - 64
EP - 77
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
ER -