= Gaussian regression score
{c}
{title2=$\dot\ell=h_\theta(X)\varepsilon/\sigma^2$}
For a <regression function> $g_\theta$, let $h_\theta=\partial_\theta g_\theta$. With <independent> centered <normal distribution> error of known <variance> $\sigma^2$, the parametric <score function> is $h_\theta(X)\varepsilon/\sigma^2$. It has zero <conditional expectation> given the <covariate>, so unknown covariate-density nuisance directions do not remove any of its <Fisher information>.
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