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
endogarray or dataframe

endogenous/response variable

exogarray 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()

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.