Multiplier-bootstrap maximum test from debiased influence scores

The function requires only coordinatewise score variances. It does not form or invert a q by q covariance matrix and therefore permits q > n.

Usage

max_test_hd(
  theta_tilde,
  target,
  psi_centered,
  alpha = 0.05,
  bootstrap_B = 999L,
  bootstrap_seed = NULL,
  multipliers = NULL,
  block_size = 256L
)

Arguments

theta_tilde: Debiased target estimates.
target: Null target vector.
psi_centered: Centered n by q influence-score matrix.
alpha: Test level.
bootstrap_B: Number of Gaussian multiplier draws.
bootstrap_seed: Optional reproducible seed. The caller's RNG state is restored after multiplier generation.
multipliers: Optional fixed n by bootstrap_B multiplier matrix.
block_size: Number of draws processed together by the C++ kernel.

Value

A list containing the observed maximum, bootstrap distribution, critical value, p-value, separate null-moment calibrations, and the backward-compatible null_energy alias for the null second moment.