Consistent model identification of varying coefficient quantile regression with BIC tuning parameter selection

Abstract

Quantile regression provides a flexible platform for evaluating covariate effects on different segments of the conditional distribution of response. As the effects of covariates may change with quantile level, contemporaneously examining a spectrum of quantiles is expected to have a better capacity to identify variables with either partial or full effects on the response distribution, as compared to focusing on a single quantile. Under this motivation, we study a general adaptively weighted LASSO penalization strategy in the quantile regression setting, where a continuum of quantile index is considered and coefficients are allowed to vary with quantile index. We establish the oracle properties of the resulting estimator of coefficient function. Furthermore, we formally investigate a BIC-type uniform tuning parameter selector and show that it can ensure consistent model selection. Our numerical studies confirm the theoretical findings and illustrate an application of the new variable selection procedure.

Tensor Response Quantile Regression with Neuroimaging Data

“…The proposed BIC‐type criterion function takes a similar form to the tuning parameter selection criterion considered by other work on quantile regression (for example, Lee et al., 2014; Zheng & Peng, 2017). We give a special treatment to the sample size component of $$L(k)$$, which is taken as $$nI_1\cdots I_m$$ instead of n .…”

A penalized approach to covariate selection through quantile regression coefficient models

“…where Dev ( ) is the explained deviance of the model (a measure of goodness-of-fit defined in the following), c n is a scaling factor that could depend on the sample size and df ( ) reflects the number of nonzero coefficients. We follow the definitions proposed by Schwarz (1978), Lee et al (2014) and Zheng and Peng (2017), and define…”