期刊
STATISTICA SINICA
卷 32, 期 2, 页码 893-914出版社
STATISTICA SINICA
DOI: 10.5705/ss.202020.0051
关键词
Extreme quantile; local linear regression; semi-parametric; single-index; tail
资金
- China Scholarship Council [201906100118]
- National Natural Science Foundations of China [11571081, 11971115, 11690012, 71531006]
- Key Laboratory for Applied Statistics of MOE, North Mormal University
- U.S. National Science Foundation (NSF)
- [DMS-1712760]
Quantifying and predicting rare events with significant societal effects is important. This paper proposes a new semiparametric approach based on the tail single-index model to achieve a better balance between model flexibility and parsimony. The proposed method involves three steps and demonstrates its asymptotic properties.
It is important to quantify and predict rare events that have significant societal effects. Existing works on analyzing such events rely mainly on either inflexible parametric models or nonparametric models that are subject to ???the curse of dimensionality.??? We propose a new semiparametric approach based on the tail single-index model to obtain a better balance between model flexibility and parsimony. The procedure involves three steps. First, we obtain a ???n-estimator of the index parameter. Next, we apply the local polynomial regression to estimate the intermediate conditional quantiles. Lastly, these quantiles are extrapolated to the tails to estimate the extreme conditional quantiles. We establish the asymptotic properties of the proposed estimators. Furthermore, we demonstrate using a simulation and an analysis of Los Angeles mortality and air pollution data that the proposed method is easy to compute and leads to more stable and accurate estimations than those of alternative methods.
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