Estimation in functional linear quantile regression

Details Estimation in functional linear quantile regression Estimation in functional linear quantile regression

2012-02-22

arxiv.org/abs/1202.4850v1

Mathematics

Statistics Theory

41pages, 8figures

Scientific paper

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 each fixed quantile index is modeled as a linear functional of the covariate. Here, we suppose that covariates are discretely observed and sampling points may differ across subjects, where the number of measurements per subject increases as the sample size. Also, 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 rates are optimal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. Empirical choice of the cut-off level is studied by using simulations.

Affiliated with

Also associated with

No associations

Rating

Estimation in functional linear quantile regression does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Estimation in functional linear quantile regression, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Estimation in functional linear quantile regression will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-414782