= Adaptivity to an unknown covariate distribution
{title2=$E[\dot\ell\mid X]=0$}
If the parametric <score function> has zero <conditional expectation> given a <covariate> $X$, it is orthogonal to the centered <functions> of $X$ that form the covariate-density <nuisance tangent space>. Its <efficient score> then equals its parametric <score function>, and the unknown covariate distribution causes no loss of <Fisher information>. This applies to <Gaussian regression scores> and more generally to regular conditional models with unrestricted covariate distribution and no additional nuisance components.
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