Bivariate quantile smoothing splines

Xuming He

doi:10.1111/1467-9868.00138

Bivariate quantile smoothing splines

2002-01-06

98

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AI

DOI：10.1111/1467-9868.00138

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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 bivariate B-splines as approximate solutions. We use real and simulated data to illustrate the methodology proposed.

Keyword:

conditional quantile

linear program

nonparametric regression

robust regression

Schwarz information criterion

tensor product spline

Bivariate quantile smoothing splines

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