Local quantile regression - Wolfgang Karl Härdle; Vladimir Spokoiny; Weining Wang (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2010)
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.
Keywords: C00; C14; J01; J31; 330; conditional quantiles; semiparametric and nonparametric methods; asymmetric Laplace distribution; exponential risk bounds; adaptive bandwidth selection; Regression; Nichtparametrisches Verfahren; Theorie