hunt_optimal: Optimal hunting

In dScoreTest: Debiased Score Tests for Goodness of Fit and Model Comparison

Optimal hunting

Description

Hunt by fitting residuals on X optimally, trained by solving a weighted least squares. The hunted function is also pre-debiased. This is the procedure of Section 2.2.1 of Dhawan, Guo and Shah (2026).

Usage

hunt_optimal(
  wls_hunt_method,
  wls_method,
  score_fun,
  weight_fun,
  fit,
  y,
  X,
  X.cols = 1:ncol(X),
  binary.y = FALSE,
  trim.outlier = TRUE,
  arg.wls_hunt_method = NULL,
  arg.wls_method = NULL,
  predict_fun = stats::predict,
  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.
wls_method	Function with signature wls_method(y, X, w, ...) that fits the null model \hat{f} \in \mathcal{F} with weighted least squares, i.e., minimizing \sum_i w_i (f(x_i) - y_i)^2. The returned object must support predict_fun(f, X) for evaluation.
score_fun	Function with signature score_fun(fit, y, X) returning a vector of scores l'(\hat{f}(x_i), y_i).
weight_fun	Function with signature weight_fun(fit, X) that computes the weight \mathbb{E}[l''(\hat{f}(x_i), y_i) | x_i] for each row x_i of X.
fit	Fitted null model. Must support predict_fun(fit, X).
y	Response vector of length n.
X	Covariates of dim n x p.
X.cols	Subset of covariates to hunt. Default 1:ncol(X).
binary.y	Set to TRUE only if y is binary (default: FALSE). This only affects how the variance function is estimated. When TRUE, predict_fun(fit, X) must return the conditional probability P(y = 1 | 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).
arg.wls_method	Named list of additional arguments passed to wls_method (default to NULL).
predict_fun	Function with signature predict_fun(fit, X) returning a numeric vector of predictions from null-model fits. Default stats::predict.
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.

Details

If y is binary, then set binary.y=TRUE. Meanwhile, predict_fun(fit, X, type="response") must output the predicted probabilities.

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 orthogonalized 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

dScoreTest documentation built on Sept. 3, 2026, 1:06 a.m.