doubleml.double_ml_score_mixins.NonLinearScoreMixin

class doubleml.double_ml_score_mixins.NonLinearScoreMixin

Mixin class implementing DML estimation for score functions being nonlinear in the target parameter

Notes

The score functions of many DML models (PLR, PLIV, IRM, IIVM) are linear in the parameter. This mixin class NonLinearScoreMixin allows to use the DML framework for models where the linearity in the parameter is not given. The mixin class implements the empirical analog of the moment condition \(\mathbb{E}(\psi(W; \theta, \eta)) = 0\), the estimation of \(\theta\) via numerical root search of the moment condition and the estimation of the corresponding asymptotic variance. For details, see the chapters on score functions and on variance estimation in the DoubleML user guide.

To implement a DML model utilizing the NonLinearScoreMixin class, the abstract methods _compute_score, which should implement the evaluation of the score function \(\psi(W; \theta, \eta)\), and _compute_score_deriv, which should implement the evaluation of the derivative of the score function \(\frac{\partial}{\partial \theta} \psi(W; \theta, \eta)\), need to be added model-specifically.

Methods