Estimation in Functional Linear Quantile Regression

• Activity Number: 345
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Kengo Kato*+
• Companies: Hiroshima University
• Keywords: functional data ; principal component analysis ; quantile regression

Abstract

This paper studies estimation in functional linear quantile regression in which the dependent variable is scalar while the covariate is a function, and the conditional quantile for a fixed quantile index is modeled as a linear functional of the covariate. We presume that covariates are discretely observed and sampling points may differ across subjects, where the number of measurements per subject increases as the sample size. We allow the quantile index to vary over a given subset of the open unit interval, so the slope function is a function of two variables: (typically) time and quantile index. Likewise, the conditional quantile function is a function of the quantile index and the covariate. We consider an estimator for the slope function based on the principal component basis. An estimator for the conditional quantile function is obtained by a plug-in method. Since the so-constructed plug-in estimator not necessarily satisfies the monotonicity constraint with respect to the quantile index, we also consider a class of monotonized estimators for the conditional quantile function. We establish rates of convergence for these estimators under suitable norms, showing that these