PPI++ One-Sample Mean Test

Performs a one-sample hypothesis test for the population mean using the PPI++ (Prediction-Powered Inference Plus) estimator with EIF-optimal lambda.

Usage

ppi_mean_test(Y_L, f_L, f_U, theta0 = 0, alpha = 0.05, lambda = NULL)

Arguments

Y_L

Numeric vector of labeled outcomes.

f_L

Numeric vector of predictions for labeled samples.

f_U

Numeric vector of predictions for unlabeled samples.

theta0

Null hypothesis value (default 0).

alpha

Significance level (default 0.05).

lambda

Optional user-specified lambda. If NULL, uses EIF-optimal lambda.

Value

A list with components:

estimate

The PPI++ point estimate of the mean.

se

Standard error of the estimate.

z_stat

Z test statistic.

p_value

Two-sided p-value.

reject

Logical indicating whether null is rejected at level alpha.

lambda

The lambda value used.

ci

Confidence interval at level 1-alpha.

Examples

set.seed(123)
n <- 100; N <- 1000
Y_L <- rnorm(n, mean = 0.5)
f_L <- Y_L + rnorm(n, sd = 0.5)
f_U <- rnorm(N, mean = 0.5) + rnorm(N, sd = 0.5)
ppi_mean_test(Y_L, f_L, f_U, theta0 = 0)
#> $estimate
#> [1] 0.5867406
#> 
#> $se
#> [1] 0.04983671
#> 
#> $z_stat
#> [1] 11.77326
#> 
#> $p_value
#> [1] 5.361031e-32
#> 
#> $reject
#> [1] TRUE
#> 
#> $lambda
#> [1] 0.720832
#> 
#> $ci
#> [1] 0.4890625 0.6844188
#>