Compute the confidence interval using Empirical Likelihood.
The parameter for which the confidence interval is desired.
The significance level. Default is 0.05.
The maximum value the upper limit can be. Default is the 99.9% confidence value under OLS assumptions.
The minimum value the lower limit can be. Default is the 99.9% confidence value under OLS assumptions.
Can either be ‘nm’ for Nelder-Mead or ‘powell’ for Powell. The optimization method that optimizes over nuisance parameters. The default is ‘nm’.
When True, the exogenous variables are assumed to be stochastic. When the regressors are nonstochastic, moment conditions are placed on the exogenous variables. Confidence intervals for stochastic regressors are at least as large as non-stochastic regressors. The default is True.
Test parameters using Empirical Likelihood.
This function uses brentq to find the value of beta where test_beta([beta], param_num) is equal to the critical value.
The function returns the results of each iteration of brentq at each value of beta.
The current function value of the last printed optimization should be the critical value at the desired significance level. For alpha=.05, the value is 3.841459.
To ensure optimization terminated successfully, it is suggested to do el_test([lower_limit], [param_num]).
If the optimization does not terminate successfully, consider switching optimization algorithms.
If optimization is still not successful, try changing the values of start_int_params. If the current function value repeatedly jumps from a number between 0 and the critical value and a very large number (>50), the starting parameters of the interior minimization need to be changed.