I am performing the quantile regression in R on a non linear model. I am getting the coefficients for the desired quantiles (tau = 0.05, 0.50, 0.95). All very nice, but running the code without reasoning is not good enough. As we determine quantiles at the extremes, i.e. 0.05, 0.95 but also smaller/larger, the regression results will be dependent on the number of points in the data sample. My questions are:
- Are there any rules for determining the minimum number of samples (sample size) needed to perform such quantile regressions?
- How do we determine the confidence LEVEL of the quantile regression, e.g. at 0.05? (Level, not interval... I mean, if I get a regression line for tau = 0.05 how much is its confidence level? Or am I thinking wrong?.. I used as tag "confidence-interval" because "confidence-Level" was not allowed)
If there is literature with indications, I will gladly read it... if possible with practical rules without complicated theorems.
Thank you all very much!