Robust local quantile regression for reference curves

Abstract

We propose two non-parametric methods to construct locally fitted quantile reference curves that are robust with respect to outliers in the predictor variable. The first includes a weighting procedure and the second, the detection and subsequent elimination of outlying predictor variable values before the local fitting process. The reference curves fitted by the proposed methods generate quantile limits that are less affected in regions with a low frequency of the predictor variable values. The proposed procedures are used to fit reference curves to data extracted from a study conducted at the Heart Institute of the University of São Paulo Medical School.