Regularized Partially Functional Quantile Regression
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Regularized Partially Functional Quantile Regression
We present a quantile regression model where the response variable is scalar while the explanatory variables involves both infinite-dimensional predictor processes-viewed as functional data, and high-dimensional scalar covariates. Despite extensive work focusing on functional linear models, there is little effort devoted to the development of robust methodologies that tackle the scenarios of non-Gaussian processes. This motivates our proposal of functional quantile regression that seeks alternative solution to least squares type procedures, within the partially functional regression framework. We focus on inferring a sparse representation of the high-dimensional covariates but the problem is complicated by the nature of functional data. To this end, we simultaneously employ two types of regularization, involving truncation and shrinkage techniques, to select and estimate relevant scalar covariates while taking the functional components into consideration. Theoretically, we show that our proposed penalized quantile estimators enjoy oracle properties such as consistency and asymptotic normality, under some mild conditions. Monte Carlo simulations support our theoretical findings and an application to brain imaging data demonstrates the advantages of our method over alternative approaches.
Handbook of Quantile Regression
Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.
Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling
Author: Ivan Jeliazkov
language: en
Publisher: Emerald Group Publishing
Release Date: 2019-10-18
Volume 40B of Advances in Econometrics examines innovations in stochastic frontier analysis, nonparametric and semiparametric modeling and estimation, A/B experiments, big-data analysis, and quantile regression.