PPI++ Mean Estimation — ppi_plusplus

Helper function for PPI++ mean estimation

Usage

ppi_plusplus_mean(
  Y_l,
  f_l,
  f_u,
  alpha = 0.05,
  alternative = "two-sided",
  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.
alpha: (scalar): type I error rate for hypothesis testing - values in (0, 1); defaults to 0.05.
alternative: (string): Alternative hypothesis. Must be one of "two-sided", "less", or "greater".
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

tuple: Lower and upper bounds of the prediction-powered confidence interval for 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(Y_l, f_l, f_u)
#>         lower    upper
#> [1,] 1.008962 1.226418