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Simultaneous estimation of quantile curves using quantile sheets. (English) Zbl 1443.62107
Summary: The results of quantile smoothing often show crossing curves, in particular, for small data sets. We define a surface, called a quantile sheet, on the domain of the independent variable and the probability. Any desired quantile curve is obtained by evaluating the sheet for a fixed probability. This sheet is modeled by \(P\)-splines in form of tensor products of \(B\)-splines with difference penalties on the array of coefficients. The amount of smoothing is optimized by cross-validation. An application for reference growth curves for children is presented.

62G08 Nonparametric regression and quantile regression
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