Weighted-least-squares hunting — hunt

Hunt by fitting residuals on X, trained by solving a weighted least squares. See Proposition 2 of Dhawan, Guo and Shah (2026).

Usage

hunt_wls(
  wls_hunt_method,
  resids,
  X,
  X.cols = 1:ncol(X),
  trim.outlier = TRUE,
  arg.wls_hunt_method = NULL,
  predict_fun_hunt = stats::predict
)

Arguments

wls_hunt_method: Function with signature wls_hunt_method(y, X, w, ...) that returns a fitted alternative model \(\hat{g} \in \mathcal{G}\) by minimizing \(\sum_i w_i (y_i - g(x_i))^2\). The returned object must support predict_fun_hunt(g, X) for evaluation.
resids: Residuals (i.e., negative scores) of length n from the null model.
X: Covariates of dim n x p.
X.cols: Subset of covariates to hunt. (Default: 1:ncol(X))
trim.outlier: If TRUE, outliers in \(\hat{h}(X)\) will be trimmed from the hunted \(\hat{h}\) using Tukey's IQR rule.
arg.wls_hunt_method: Named list of additional arguments passed to wls_hunt_method (default to NULL).
predict_fun_hunt: Function with signature predict_fun_hunt(fit, X) returning a numeric vector of predictions from the alternative-model fit. Default stats::predict.

Value

An object of class "hunt", a list with elements:

hunt.fit: The fitted hunt model produced by wls_hunt_method.
trim.bounds: The Tukey IQR trimming bounds, or c(-Inf, Inf) when trim.outlier = FALSE.
predict_fun_hunt: The prediction function for hunt.fit, as supplied.
X.cols: The columns of X used for the hunt, as supplied.
h: A function with signature h(X) giving the hunted signal.

References

Dhawan, A., Guo, F. R. and Shah, R. D. (2026). The debiased score test: hunt-and-test for semiparametric hypotheses. arXiv:2607.28861. https://arxiv.org/abs/2607.28861