Additive Models for Quantile Regression

Additive Models for Quantile Regression: Model Selection and Confidence Bandaids

We describe some recent development of nonparametric methods for estimating conditional quantile functions using additive models with total variation roughness penalties. We focus attention primarily on selection of smoothing parameters and on the construction of confidence bands for the nonparametric components. Both pointwise and uniform confidence bands are introduced; the uniform bands are based on the Hotelling (1939) tube approach. Some simulation evidence is presented to evaluate finite sample performance and the methods are also illustrated with an application to modeling childhood malnutrition in India. The methods described have been implemented in the R package {\tt quantreg}.



The paper is available in pdf. Some notes on Hotelling tubes are also available here. R code for the simulations reported in the paper are available here. as a gzipped tar archive. The data for the application to malnutrition in India is available here. as an R binary data file. Slides for a talk about all this are available here..

A more recent note, in the form of an R vineagrette about lambda selection for a group lasso proposal of Kato (2011) is available here..

An even more recent note on some connections to inference for frontier production models for a Festschrift volume dedicated to Peter Schmidt is available here.. Software in R to reproduce the results in this paper is available in tar.gz compressed form here..
Comments are, of course, always welcome.