PPI++ Mean Estimation (Point Estimate)

Helper function for PPI++ mean estimation (point estimate)

Usage

ppi_plusplus_mean_est(
  Y_l,
  f_l,
  f_u,
  lhat = NULL,
  coord = NULL,
  w_l = NULL,
  w_u = NULL
)

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.

lhat

(float, optional): Power-tuning parameter (see https://arxiv.org/abs/2311.01453). The default value, NULL, will estimate the optimal value from the data. Setting lhat = 1 recovers PPI with no power tuning, and setting lhat = 0 recovers the classical point estimate.

coord

(int, optional): Coordinate for which to optimize lhat = 1. If NULL, it optimizes the total variance over all coordinates. Must be in (1, ..., d) where d is the dimension of the estimand.

w_l

(ndarray, optional): Sample weights for the labeled data set. Defaults to a vector of ones.

w_u

(ndarray, optional): Sample weights for the unlabeled data set. Defaults to a vector of ones.

Value

float or ndarray: Prediction-powered point estimate of the mean.

Details

PPI++: Efficient Prediction Powered Inference (Angelopoulos et al., 2023) https://arxiv.org/abs/2311.01453

Examples

dat <- simdat(model = "mean")

form <- Y - f ~ 1

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_plusplus_mean_est(Y_l, f_l, f_u)
#> [1] 1.099237