# 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.

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` Names of endogenous variables `exog_names` Names of exogenous variables

Methods

 `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`() `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.

Methods

 `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`() `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` Names of endogenous variables `exog_names` Names of exogenous variables