Brute-Force Higher-Order Influence Function Estimator (Test Version)

Computes the order-m higher-order influence function (HOIF) term using an explicit enumeration of all ordered index tuples.

compute_HOIF_test(
  X,
  A,
  Y,
  mu1,
  mu0,
  pi,
  m,
  sample_splitting = 0,
  n_folds = 2,
  seed
)

Arguments

X

Covariate matrix (n × p).

A

Binary treatment indicator vector.

Y

Outcome vector.

mu1

Estimated outcome regression under treatment.

mu0

Estimated outcome regression under control.

pi

Estimated propensity scores.

m

Order of the HOIF term.

sample_splitting

Whether to use K-fold sample splitting (0 = no).

n_folds

Number of folds for sample splitting.

seed

Random seed for reproducibility.

Value

A list with elements:

IIFF_1_m

Order-m influence function term for treated units

IIFF_0_m

Order-m influence function term for control units

Details

🚨 **This implementation is intentionally naive and is provided solely for validation and debugging purposes.** It should only be used on very small datasets to verify the correctness of optimized implementations.

The computational complexity grows factorially with both sample size and order m.

This function directly implements the combinatorial definition of the HOIF using full enumeration of index permutations. Matrix inverses are computed explicitly and no numerical stabilization is included.

This function is part of the package's **internal test infrastructure** and should not be exported or used in applied analysis.