# Quantile regression power analysis

New to the site and to stats here! This may be a silly question, but I haven't been able to find a satisfactory answer on the procedure for a power analysis (or general guidelines about sample size) with a quantile regression. I plan on looking at 3 predictors along a single outcome. What would a recommended sample size be, or how can I conduct a power analysis? I appreciate any help, thanks!

For general linear quantile models of the form $$F^{-1}_{Y|X}(\tau) = X'\beta_n(\tau)$$ where $\beta_n$ is allowed to depend on the sample size, Chernozhukov and Fernandez-Val (2005) construct a power analysis for conditional quantile regression models as in your case. They consider the general null hypothesis $$R(\tau)\beta_0 (\tau) - r(\tau) = 0$$ for $\tau \in (0,1)$. Their procedure allows you to test for
Victor Chernozhukov makes his R code available on his website under the section "Policy Analysis" for the paper "Subsampling on Quantile Regression Processes".