statsmodels: Method used to generate condifence intervals for quantile regression coefficients?
Inference for parameters is the same across models and is mostly inherited from the base classes.
Quantile regression has a model specific covariance matrix of the parameters.
tvalues, pvalues, confidence intervals, t_test and wald_test are all based on the assumption of an asymptotic normal distribution of the estimated parameters with the given covariance, and are "generic".
Linear models like OLS and WLS, and optionally some other models can use the t and F distribution instead of normal and chisquare distribution for the Wald test based inference.
specifically conf_int is defined in statsmodels.base.models.LikelihoodModelResults
partial correction:
QuantReg uses t and F distributions for inference, since it is currently treated as a linear regression model, and not normal and chisquare distributions as the related M-estimators, RLM, in statsmodels.robust.
Most models have now a use_t option to choose the inference distributions, but it hasn't been added to QuantReg.
I am using the statsmodels.formulas.api.quantreg() for quantile regression in Python. I see that when fitting the quantile regression model, there is an option to specify the significance level for confidence intervals of the regression coefficients, and the confidence interval result appears in the summary of the fit.
What statistical method is being used to generate confidence intervals about the regression coefficients? It does not appear to be documented and I've dug through the source code for quantile_regression.py and summary.py to find this with no luck. Can anyone shed some light on this?