Data Integration in High Dimension With Multiple Quantiles

Abstract

This article deals with the analysis of high dimensional data that come from multiple sources ("experiments") and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may be different across experiments. We introduce a new regression approach with multiple quantiles to select those predictors that affect any of the responses at any quantile level and to estimate the nonzero parameters. Our approach differs from established methods by being able to handle heterogeneity in data sets as well as heavy-tailed error distributions, two difficulties that are often encountered in complex data scenarios. Our estimator is a minimizer of a penalized objective function, which aggregates the data from the different experiments. We establish model selection consistency and asymptotic normality of the estimator. In addition we present an information criterion, which can also be used for consistent model selection. Simulations and two data applications illustrate the advantages of our method in recovering the underlying regression models, which comes from taking the group structure induced by the predictors across experiments and quantile levels into account.

Penalized Regression with Multiple Loss Functions and Variable Selection by Voting

“…represents the solution of (2.6) with λ n,k = λ. This type of Bayesian information criteria is a fairly popular tool for selecting the tuning parameter in penalized regression (Chen and Chen, 2008;Wang et al, 2009;Kim et al, 2012;Wang et al, 2013;Lee et al, 2014;Peng and Wang, 2015;Sherwood and Wang, 2016;Dai et al, 2023). Alternatively one could use cross validation to determine λ n,k .…”

Transfer Learning for High-Dimensional Quantile Regression via Convolution Smoothing

“…Moreover, large-scale covariance matrix estimation is needed in their method. In the field of data integration, Dai et al (2023) proposed to use multiple datasets together with multiple quantiles to select variables simultaneously. They established model selection consistency and asymptotic normality of their estimator, but theoretical results about the estimation error are left unknown.…”