Reference Curves Estimation Using Conditional Quantile and Radial Basis Function Network with Mass Constraint

Abstract

This paper focuses on the improvement of reference curves building \(Y=q(X)\) using a fast algorithm, robust against outliers. Our method consists in plugging a radial basis function neural network in the local linear quantile regression estimation proposed by Yu and Jones (QYJ). This neural network (QRBFc) is designed with a constructive algorithm, introducing a constraint on its integral over the input space. After explaining the different models and algorithms, we compare the QYJ and QRBFc estimators with the quantile regression neural network (QRNN) implemented by A. J. Cannon through simulations with a known underlying model using the R software. We observe that the QRBFc estimator reduces the mean absolute deviation error obtained with other estimators by about 16 %, the introduction of the constraint allowing to lower the number of neurons and therefore the computation time. Finally, using a database of 416 electroencephalograms recorded on preterm infants, we compare the QYJ, QRBFc and QRNN models for the building of brain maturation curves which are based on the dependence of the mean duration of interburst intervals (called IBIs—periods of quiescence between periods of normal electrical activity) with the age. The pathological infants represent 12 % of the total population. Denoting by \(S_A\) the set of individuals whose coordinates (age, mean IBI length) are above the \(90~\%\)-quantile curve, the QRBFc network improves by \(16.5~\%\) the number of pathological infants in \(S_A\) compared to QYJ, when QRNN proved to be too unstable.