Bivariate quantile smoothing splines
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1998 · Volume 60 · Issue 3
Abstract
It has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample. We introduce bivariate quantile smoothing splines, which belong to the space of bilinear tensor product splines, as nonparametric estimators for the conditional quantile functions in a two-dimensional design space. The estimators can be computed by using standard linear programming techniques and can further be used as building-blocks for conditional quantile estimations in higher dimensions. For moderately large data sets, we recommend penalized bivariateB-splines as approximate solutions. We use real and simulated data to illustrate the methodology proposed.
Keywords
Conditional quantile, Linear program, Nonparametric regression, Robust regression, Schwarz information criterion, Tensor product spline
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