PPI Quantile Estimation

Helper function for PPI quantile estimation

Usage

ppi_quantile(Y_l, f_l, f_u, q, alpha = 0.05, exact_grid = FALSE)

Arguments

Y_l

(vector): n-vector of labeled outcomes.

f_l

(vector): n-vector of predictions in the labeled data.

f_u

(vector): N-vector of predictions in the unlabeled data.

q

(float): Quantile to estimate. Must be in the range (0, 1).

alpha

(scalar): type I error rate for hypothesis testing - values in (0, 1); defaults to 0.05.

exact_grid

(bool, optional): Whether to compute the exact solution (TRUE) or an approximate solution based on a linearly spaced grid of 5000 values (FALSE).

Value

tuple: Lower and upper bounds of the prediction-powered confidence interval for the quantile.

Details

Prediction Powered Inference (Angelopoulos et al., 2023) https://www.science.org/doi/10.1126/science.adi6000

Examples

dat <- simdat(model = "quantile")

form <- Y - f ~ X1

Y_l <- dat[dat$set == "labeled", all.vars(form)[1]] |> matrix(ncol = 1)

f_l <- dat[dat$set == "labeled", all.vars(form)[2]] |> matrix(ncol = 1)

f_u <- dat[dat$set == "unlabeled", all.vars(form)[2]] |> matrix(ncol = 1)

ppi_quantile(Y_l, f_l, f_u, q = 0.5)
#> [1] 0.9160743 1.3043746