# Quantile Regression and False Discovery

Context: quantile regression with a binary predictor, but this question can be generalized to other quantile regression model structures and possibly splines/adaptive models.

In quantile regression there appears to be repeated testing for selected quant values in regards to the estimated dependent variable. I have not seen mention of correcting alpha levels for false discovery given the repeated testing. Is this a concern and what have others seen in this area?

Thank you.

EDIT: Example figure below (right pane) where estimates and ttests are calculated for quantile = (0.05 0.25 0.50, 0.75, 0.9). So, a ttest gets calculated for these 5 quant values (e.g., quantiile: 0.05, p-value: <0.9999,...,quantile: 0.9; pvalue: 0.0314)

• Can you post more about where you see this repeated testing happen? – eric_kernfeld May 8 '18 at 18:23
• Here is a toy example I created were estimates are generated for quantile = (0.05 0.25 0.50, 0.75, 0.9). So, a ttest gets calculated for these 5 quant values (e.g., quantiile: 0.05, p-value: <0.9999,...,quantile: 0.9; pvalue: 0.0314). – hlsmith May 8 '18 at 18:56
• What algorithm or software package did you use to run that example? – eric_kernfeld May 8 '18 at 21:01
• I would also be interested to see what you come up with as an answer to this question, since it was one I tried to find an answer to several months ago but came up flat. Seems that there is very little literature on the subject of type I error adjustment in the quantile regression setting. Adjustment will certainly be complicated due to the fact that the parameter estimates at different quantiles will likely have a rather complex correlation structure. (1/2) – Ryan Simmons May 8 '18 at 21:35
• (2/2) In practice, I find, most people that use quantile regression aren't particularly interested in point-wise significance testing at each quantile, so much as they are interested in looking at the trend and pattern of parameter estimates across the range of quantiles. To that end, it may be of more interest to calculate some sort of simultaneous confidence (or prediction) band for the set of estimates across quantiles rather than relying on a series of pointwise confidence intervals as done here. Of course, coding this may be difficult. – Ryan Simmons May 8 '18 at 21:40