class statsmodels.regression.quantile_regression.QuantReg(endog, exog, **kwargs)[source]

Quantile Regression

Estimate a quantile regression model using iterative reweighted least squares.

  • endog (array or dataframe) – endogenous/response variable
  • exog (array or dataframe) – exogenous/explanatory variable(s)


The Least Absolute Deviation (LAD) estimator is a special case where quantile is set to 0.5 (q argument of the fit method).

The asymptotic covariance matrix is estimated following the procedure in Greene (2008, p.407-408), using either the logistic or gaussian kernels (kernel argument of the fit method).



  • Birkes, D. and Y. Dodge(1993). Alternative Methods of Regression, John Wiley and Sons.
  • Green,W. H. (2008). Econometric Analysis. Sixth Edition. International Student Edition.
  • Koenker, R. (2005). Quantile Regression. New York: Cambridge University Press.
  • LeSage, J. P.(1999). Applied Econometrics Using MATLAB,

Kernels (used by the fit method):

  • Green (2008) Table 14.2

Bandwidth selection (used by the fit method):

  • Bofinger, E. (1975). Estimation of a density function using order statistics. Australian Journal of Statistics 17: 1-17.
  • Chamberlain, G. (1994). Quantile regression, censoring, and the structure of wages. In Advances in Econometrics, Vol. 1: Sixth World Congress, ed. C. A. Sims, 171-209. Cambridge: Cambridge University Press.
  • Hall, P., and S. Sheather. (1988). On the distribution of the Studentized quantile. Journal of the Royal Statistical Society, Series B 50: 381-391.

Keywords: Least Absolute Deviation(LAD) Regression, Quantile Regression, Regression, Robust Estimation.


fit([q, vcov, kernel, bandwidth, max_iter, …]) Solve by Iterative Weighted Least Squares
from_formula(formula, data[, subset, drop_cols]) Create a Model from a formula and dataframe.
get_distribution(params, scale[, exog, …]) Returns a random number generator for the predictive distribution.
hessian(params) The Hessian matrix of the model
information(params) Fisher information matrix of model
initialize() Initialize (possibly re-initialize) a Model instance.
loglike(params) Log-likelihood of model.
predict(params[, exog]) Return linear predicted values from a design matrix.
score(params) Score vector of model.
whiten(data) QuantReg model whitener does nothing: returns data.


df_model The model degree of freedom, defined as the rank of the regressor matrix minus 1 if a constant is included.
df_resid The residual degree of freedom, defined as the number of observations minus the rank of the regressor matrix.
endog_names Names of endogenous variables
exog_names Names of exogenous variables