(rqpd) How to obtain the confidence intervals of a quantile regression model on panel data? I had to adjust a quantile regression model on panel data and I used the rqdp package, however, when I needed the confidence intervals, I realized that the package does not provide the item in question. It just says that I can build the standard errors through the boot.rqpd() function. Does anyone have any suggestions on how to proceed. I leave the routine and data below.
path = 'https://raw.githubusercontent.com/jacksonMaike/analises-r/master/datasets/'
dat = read.csv(paste0(path, 'dataset-covid-v04.csv'))
head(dat)

if(!suppressMessages(require(rqpd))) install.packages("rqpd")
library(rqpd)

taus = c(.025,.05,.075,.1,.15,.2,.25,.5,.75,.8,.85,.9,.925,.95,.975)
fit = rqpd(Returns ~ Returns_t_1 + Returns_t_1:Lim_t_1 + SP + SP:Dcovid +
             GSI + GSI:Dcovid | factor(ID),
           panel(taus = taus,
                 tauw  = rep(1/15, 15)),
           data = dat)
summary.rqpd(fit)

Thanks in advance!
 A: Which type of bootstrap depends on the problem type. What one has to avoid for quantile analysis is any type of repetition of the bootstrap results or the quantile results may be unreliable especially if wider confidence intervals are desired, e.g., 95%. This would be less of a problem for model-based bootstrap, wherein repetition is rare than it would be if one is resampling a small number for $N$.
In r, one uses a quantile command for the left and right quantiles needed for constructing a confidence interval. https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/quantile.
In Mathematica the command would be
Quantile[data, 0.025, $\{\{0, 1\}, \{0, 1\}\}$]
to extrapolate a 2.5% left tail using the Weibull method, but with  few data entries an 80% CI might be more reliable. For $n=15$ data entries, the Weibull method would assign an $\frac{n-1}{n+1}$=87.5% confidence interval for the min to max values. In Excel, that command would be PERCENTILE.EXC(A1:A40,0.025), where at least 40 data entries are required for 95% tails as Excel will not extrapolate.
In general, there are many methods of finding confidence intervals and see https://mathworld.wolfram.com/Quantile.html for an outline of nine of them. In r, there are also nine of them listed in https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/quantile. These differ by the type of extrapolated tail formulas used. In some cases, extrapolation of tails would not make sense. For example, if the data is left and right truncated the maximum confidence interval ends at the truncation points, and in Excel one would then use PERCENTILE.INC in some cases.
