Valid Inference on Multiple Quantile Regressions.

quasar

quasar is an R package that provides valid inference procedures when multiple quantile regressions are fitted simultaneously.
It implements the rank-score–based closed testing approach proposed in:

De Santis, F., Vesely, A., and Andreella, A. (2025)
Inference on Multiple Quantiles in Regression Models by a Rank-Score Approach.

Installation

To install the development version from GitHub:

# install.packages("remotes")
remotes::install_github("angeella/quasar")

Toy Example

library(quasar)
library(quantreg)

# Set the dimension of the covariates
p <- 3
Sigma <- diag(p)

# Simulate data
dat_n <- simulateData(
  n            = 200,
  beta         = 0,
  gamma        = c(0.2, -0.1),
  mu           = 4,
  Sigma        = Sigma,
  sigma.y      = 0.5,
  distribution = "t"
)

# Fit quantile regressions
mod <- rq(
  y ~ X + Z1 + Z2,
  tau  = c(0.1, 0.25, 0.5, 0.75, 0.9),
  data = dat_n
)

# Perform closed testing based on rank-score statistics
closedTesting(mod, X = "X")

Simulation Code

The R scripts used to reproduce the simulation studies (Figures 2, 3, 4 and 5 in the paper)
are available in the simulations/ folder of this repository.

Bugs and Feedback

Did you find some bugs?
Please write to angela.andreella[at]unive[dot]it
or open an issue on the GitHub Issues page,
preferably including a reproducible example created with the reprex package.

License

GPL (≥ 3)

Citation

If you use quasar in your research, please cite:

De Santis, F., Vesely, A., and Andreella, A. (2026).
Inference on Multiple Quantiles in Regression Models by a Rank-Score Approach.