Dj8dZddlZddlZddlmZddlmZddlmZddl m Z ddl m Z m Z mZddlmZmZGdd e Zd ZiZd ed <d ed<ded<ej*ed<eed<ddZdZddZGdde Zy)aM Quantile regression model Model parameters are estimated using iterated reweighted least squares. The asymptotic covariance matrix estimated using kernel density estimation. Author: Vincent Arel-Bundock License: BSD-3 Created: 2013-03-19 The original IRLS function was written for Matlab by Shapour Mohammadi, University of Tehran, 2008 (shmohammadi@gmail.com), with some lines based on code written by James P. Lesage in Applied Econometrics Using MATLAB(1999).PP. 73-4. Translated to python with permission from original author by Christian Prinoth (christian at prinoth dot name). N)pinv)norm)cache_readonly)RegressionModelRegressionResultsRegressionResultsWrapper)ConvergenceWarningIterationLimitWarningc4eZdZdZfdZdZ ddZxZS)QuantRegaQuantile 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. 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