I am performing the quantile regression in R on a non linear model (that is done by using nlrq). 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 a good practice. As we determine quantiles at the extremes, i.e. 0.05, 0.95 (but they can also be smaller or larger.. for example tau = 0.0001), the regression results will be dependent on the number of points in the data sample (Also the coefficients will be more sensitive on the initial given value in the nlrq function). My questions are:
- Are there any rules for determining the minimum number of samples (sample size) needed to perform such quantile regressions (I mean then for every possible tau (from 0.0001 to 0.999)?
- 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 and I should look for the confidence interval/band?.. 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!