Local quantile regression

Vladimir Spokoiny, Weining Wang, Wolfgang Karl Härdle

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

Quantile regression is a technique to estimate conditional quantile curves. It provides a comprehensive picture of a response contingent on explanatory variables. In a flexible modeling framework, a specific form of the conditional quantile curve is not a priori fixed. This motivates a local parametric rather than a global fixed model fitting approach. A nonparametric smoothing estimator of the conditional quantile curve requires to balance between local curvature and stochastic variability. In this paper, we suggest a local model selection technique that provides an adaptive estimator of the conditional quantile regression curve at each design point. Theoretical results claim that the proposed adaptive procedure performs as good as an oracle which would minimize the local estimation risk for the problem at hand. We illustrate the performance of the procedure by an extensive simulation study and consider a couple of applications: to tail dependence analysis for the Hong Kong stock market and to analysis of the distributions of the risk factors of temperature dynamics.

Original languageEnglish
Pages (from-to)1109-1129
Number of pages21
JournalJournal of Statistical Planning and Inference
Volume143
Issue number7
DOIs
Publication statusPublished - Jul 2013
Externally publishedYes

Keywords

  • Adaptive bandwidth selection
  • Excess bound
  • Local MLE
  • Propagation condition

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