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Conditional quantile analysis when covariates are functions, with application to growth data
Author(s) -
Chen Kehui,
Müller HansGeorg
Publication year - 2012
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2011.01008.x
Subject(s) - covariate , quantile regression , quantile , conditional probability distribution , curse of dimensionality , functional data analysis , functional principal component analysis , econometrics , flexibility (engineering) , mathematics , conditional expectation , computer science , statistics
Summary. 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.