Conditional Quantile Analysis When Covariates are Functions, with Application to Growth Data

• 成果类型: Article
• 署名作者: Chen, Kehui; Mueller, Hans-Georg
• 署名单位: University of California System; University of California Davis
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2011.01008.x
• 发表日期: 2012
• 页码: 67-89
• 关键词: GENERALIZED LINEAR-MODELS; Nonparametric Regression; CLASSIFICATION; spurts; charts

摘要

Motivated by the conditional growth charts problem, we develop a method for conditional quantile analysis when predictors take values in a functional space. The method proposed aims at estimating conditional distribution functions under a generalized functional regression framework. This approach facilitates balancing of model flexibility and the curse of dimensionality for the infinite dimensional functional predictors. Its good performance in comparison with other methods, both for sparsely and for densely observed functional covariates, is demonstrated through theory as well as in simulations and an application to growth curves, where the method proposed can, for example, be used to assess the entire growth pattern of a child by relating it to the predicted quantiles of adult height.