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Optimal hunting

Source: R/hunt.R
hunt_optimal.Rd

Hunt by fitting residuals on X optimally, trained by solving a weighted least squares. The hunted function is also pre-debiased.

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.

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 orthogonalised hunted signal.

Details

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