Improved Centile Estimation by Transformation And/Or Adaptive Smoothing of the Explanatory Variable

ABSTRACT A popular approach to growth reference centile estimation is the LMS (Lambda‐Mu‐Sigma) method, which assumes a parametric distribution for response variable and fits the location, scale and shape parameters of the distribution of as smooth functions of explanatory variable . This article provides two methods, transformation and adaptive smoothing, for improving the centile estimation when there is high curvature (i.e., rapid change in slope) with respect to in one or more of the distribution parameters. In general, high curvature is reduced (i.e., attenuated or dampened) by smoothing. In the first method, is transformed to variable to reduce this high curvature, and the distribution parameters are fitted as smooth functions of . Three different transformations of are described. In the second method, the distribution parameters are adaptively smoothed against by allowing the smoothing parameter itself to vary continuously with . Simulations are used to compare the performance of the two methods. Three examples show how the process can lead to substantially smoother and better fitting centiles.