Jon D. Richards Brian S. Cade 2006 <p>A drop in dispersion, <i class="EmphasisTypeItalic ">F</i>-ratio like, permutation test (<i class="EmphasisTypeItalic ">D</i>) for linear quantile regression estimates (0≤τ≤1) had relative power ≥1 compared to quantile rank score tests (<i class="EmphasisTypeItalic ">T</i>) for hypotheses on parameters other than the intercept. Power was compared for combinations of sample sizes (<i class="EmphasisTypeItalic ">n</i>=20−300) and quantiles (τ=0.50−0.99) where both tests maintained valid Type I error rates in simulations with <i class="EmphasisTypeItalic ">p</i>=2 and 6 parameters in homogeneous and heterogeneous error models. The <i class="EmphasisTypeItalic ">D</i> 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 <i class="EmphasisTypeItalic ">D</i> and rank score tests maintained correct Type I error rates, we identified regions at smaller <i class="EmphasisTypeItalic ">n</i> 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.</p> application/pdf 10.1198/108571106X96835 en Springer A permutation test for quantile regression article