Härdle, Wolfgang Karl Spokoiny, Vladimir Wang, Weining
Year of Publication:
SFB 649 discussion paper 2011-005
Conditional quantile curves provide a comprehensive picture of a response contingent on explanatory variables. Quantile regression is a technique to estimate such curves. In a flexible modeling framework, a specific form of the quantile is not a priori fixed. Indeed, the majority of applications do not per se require specific functional forms. This motivates a local parametric rather than a global fixed model fitting approach. A nonparametric smoothing estimate of the conditional quantile curve requires to consider a balance between local curvature and variance. In this paper, we analyze a method based on a local model selection technique that provides an adaptive estimate. Theoretical properties on mimicking the oracle choice are offered and applications to stock market and weather analysis are presented.
conditional quantiles semiparametric and nonparametric methods asymmetric Laplace distribution exponential risk bounds adaptive bandwidth selection