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A permutation test for quantile regression

January 1, 2006

A drop in dispersion, F-ratio like, permutation test (D) for linear quantile regression estimates (0≤τ≤1) had relative power ≥1 compared to quantile rank score tests (T) for hypotheses on parameters other than the intercept. Power was compared for combinations of sample sizes (n=20−300) and quantiles (τ=0.50−0.99) where both tests maintained valid Type I error rates in simulations with p=2 and 6 parameters in homogeneous and heterogeneous error models. The D test required two modifications of permuting residuals from null, reduced parameter models to maintain correct Type I error rates when null models were constrained through the origin or included multiple parameters. A double permutation scheme was used when null models were constrained through the origin and all but 1 of the zero residuals were deleted for null models with multiple parameters. Although there was considerable overlap in sample size, quantiles, and hypotheses where both the D and rank score tests maintained correct Type I error rates, we identified regions at smaller n and more extreme quantiles where one or the other maintained better error rates. Confidence intervals on parameters for an ecological application relating Lahontan cutthroat trout densities to stream channel width:depth were estimated by test inversion, demonstrating a smoother pattern of slightly narrower intervals across quantiles than those provided by the rank score test.

Publication Year 2006
Title A permutation test for quantile regression
DOI 10.1198/108571106X96835
Authors Brian S. Cade, Jon D. Richards
Publication Type Article
Publication Subtype Journal Article
Series Title Journal of Agricultural, Biological, and Environmental Statistics
Index ID 1015122
Record Source USGS Publications Warehouse
USGS Organization Fort Collins Science Center