= Nuisance function
A <nuisance function> is an unknown <function> needed to identify or estimate a target <statistical parameter> but not itself the primary estimand. In treatment-effect estimation, examples are the <propensity score> $e(x)=\mathbb P(A=1\mid X=x)$ and the outcome-regression <functions> $m_a(x)=\mathbb E[Y\mid A=a,X=x]$.
These <functions> can be infinite-dimensional even when the target is one number. Estimating them poorly can bias that target, so nuisance does not mean irrelevant. <Doubly robust estimation> and <Neyman orthogonality> control certain nuisance errors, while <cross-fitting> separates training observations from score evaluation. None of these devices removes the identification assumptions needed to interpret an observational treatment comparison causally.<Double Debiased Machine Learning for Treatment and Structural Parameters by Victor Chernozhukov and others>[Introduction and Section 2, target and nuisance parameters]{ref}
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