linearmodels.panel.results.FamaMacBethResults.f_statistic_robust¶

property FamaMacBethResults.f_statistic_robust : WaldTestStatistic¶

Joint test of significance for non-constant regressors

Returns:¶

Statistic value, distribution and p-value

Return type:¶

linearmodels.shared.hypotheses.WaldTestStatistic

Notes

Implemented as a Wald test using the estimated parameter covariance, and so inherits any robustness that the choice of covariance estimator provides.

\[W = \hat{\beta}_{-}' \hat{\Sigma}_{-}^{-1} \hat{\beta}_{-}\]

where \(\hat{\beta}_{-}\) does not include the model constant and \(\hat{\Sigma}_{-}\) is the estimated covariance of the parameters, also excluding the constant. The test statistic is distributed as \(\chi^2_{k}\) where k is the number of non- constant parameters.

If debiased is True, then the Wald statistic is divided by the number of restrictions and inference is made using an \(F_{k,df}\) distribution where df is the residual degree of freedom from the model.