# statsmodels.regression.quantile_regression.QuantReg¶

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

Quantile Regression

Estimate a quantile regression model using iterative reweighted least squares.

Parameters: endog : array or dataframe endogenous/response variable exog : array or dataframe exogenous/explanatory variable(s)

Notes

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).

References

General:

• 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.

Methods

 fit([q, vcov, kernel, bandwidth, max_iter, ...]) Solve by Iterative Weighted Least Squares fit_regularized([method, maxiter, alpha, ...]) Return a regularized fit to a linear regression model. from_formula(formula, data[, subset]) Create a Model from a formula and dataframe. hessian(params) The Hessian matrix of the model information(params) Fisher information matrix of model initialize() 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.

Attributes

 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 exog_names

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