Statistical robustness usually costs efficiency. Protect against heavy tails and you lose power under Gaussianity. Accommodate heteroscedasticity and you waste degrees of freedom when errors are homoscedastic. The trade-off is so well-established that “robust statistics” is practically defined by it.
Outrigger local polynomial regression (arXiv:2603.11282) breaks the trade-off. The method incorporates an estimate of the conditional score function — the gradient of the log-likelihood of the error distribution — drawn from a wider data window than the standard estimator uses. The theoretical guarantee: the asymptotic ratio of worst-case risks between outrigger and standard estimators is at most 1, with equality if and only if the conditional error distribution is Gaussian.
The insurance is free. Under Gaussian errors, the outrigger matches standard performance exactly. Under any non-Gaussian distribution, it strictly improves. The method does not require knowing what the non-Gaussianity looks like. It does not require error-covariate independence. It does not even require symmetric conditional error distributions.
How does a method achieve robustness without paying the usual efficiency tax? By incorporating information that standard methods ignore. The conditional score function encodes the shape of the error distribution at each covariate value. Standard local polynomial regression assumes this shape is Gaussian and discards the evidence. The outrigger estimates it and uses it. Under Gaussianity, the score function carries no additional information — it's redundant with the least-squares objective — so the outrigger reduces to the standard estimator. Under anything else, the score function carries information the standard estimator is blind to.
The cost of robustness was never intrinsic. It was an artifact of ignoring available data.