Conditional-Gaussian exact-null maximum partial-t test — max_score_test

This convenience function runs exactly the same full-model pilot and maximum test used by fit_partial_sqrt_lasso_shrinkage() and returns the inference component. The default is the conditional-Gaussian exact-null maximum partial-t test; it is not a Wald, chi-square, or joint partial-F test.

Usage

max_score_test_hd(
  X,
  y,
  core_set,
  tested_set = NULL,
  lambda = NULL,
  penalty_loadings = NULL,
  all_x_penalty_loadings = NULL,
  standardize_y = NULL,
  threshold_eta = NULL,
  assume_independent = FALSE,
  alpha = 0.05,
  bootstrap_B = 999L,
  bootstrap_seed = NULL,
  bootstrap_multipliers = NULL,
  bootstrap_block_size = 256L,
  max_iter = 30000L,
  tol = 5e-06,
  check_every = 50L,
  verbose = FALSE,
  full_beta_init = NULL,
  full_operator_norm = NULL,
  null_geometry = NULL,
  rank_tolerance = 1e-10,
  test_calibration = c("conditional_gaussian", "residual_multiplier"),
  shrinkage_calibration = c("inverse_moment", "second_moment"),
  gaussian_draws = NULL,
  full_endpoint = c("thresholded_partial_debiased", "profiled_square_root_lasso",
    "all_x_square_root_lasso")
)

Arguments

X: Numeric n by p design matrix.
y: Numeric response vector.
core_set: Prespecified one-based indices of the low-dimensional core. It must contain fewer than n columns and must not be chosen from y without sample splitting.
tested_set: Prespecified high-dimensional null block. By default it is the complement of core_set; together the two sets must partition X.
lambda: Positive square-root-LASSO penalty. The default is 1.1 * sqrt(2 * log(2 * p) / n) for the all-X endpoint and 1.1 * sqrt(2 * log(2 * q) / n) for a legacy partial endpoint.
penalty_loadings: Optional positive loadings for the tested block. The default is the empirical norm of each tested column after projection off the core.
all_x_penalty_loadings: Optional length-p positive loadings for full_endpoint = "all_x_square_root_lasso". The default penalizes all columns equally. No core coefficient is exempted from the FM penalty.
standardize_y: Whether to center and scale y before fitting. It is fixed at TRUE for the all-X endpoint and must remain FALSE for the legacy endpoints. X is always centered and scaled. The standardized intercept is exactly zero; returned coefficients and prediction intercepts are back-transformed to the original data scale.
threshold_eta: Positive marginal exceedance budget for the thresholded debiased full endpoint. The threshold is qnorm(1 - threshold_eta / (2 * q)). The default is min(5, q / 2), which gives the prespecified finite-sample budget 5 in the advertised ultra-high-dimensional designs. This is a PFER-style tuning interpretation, not an FDR guarantee. The vanishing sequence 1 / log(q) is retained for theoretical and sensitivity analyses. This argument must remain NULL for either unthresholded square-root-LASSO endpoint because no coefficient threshold is applied there.
assume_independent: Must be TRUE for the default thresholded partial-debiased FM endpoint. It records the Gaussian-iid (or otherwise prespecified diagonal population precision) condition used by that endpoint. It is not required by either unthresholded square-root-LASSO endpoint or by the conditional-Gaussian exact-null test.
alpha: Test level.
bootstrap_B: Number of Gaussian multiplier draws.
bootstrap_seed: Optional seed that leaves the caller RNG unchanged.
bootstrap_multipliers: Optional reusable n by bootstrap_B matrix. Under the default conditional-Gaussian calibration it is accepted as a backward-compatible alias for gaussian_draws; under test_calibration = "residual_multiplier" it contains the multiplier draws used by the legacy test.
bootstrap_block_size: Number of draws processed per C++ block.
max_iter: Maximum primal-dual iterations.
tol: Solver convergence tolerance.
check_every: Iteration interval for diagnostics.
verbose: Print periodic solver diagnostics.
full_beta_init: Optional original-scale length-p warm start.
full_operator_norm: Optional cached operator norm of the full standardized design for the all-X endpoint or of the residualized tested design for a legacy partial endpoint.
null_geometry: Optional cached geometry returned in a previous fit on exactly the same design and partition.
rank_tolerance: Relative numerical-rank tolerance for the core SVD.
test_calibration: Test calibration. The default "conditional_gaussian" is the finite-sample exact-null Gaussian max-partial-t calibration. "residual_multiplier" retains the legacy partial-debiased multiplier maximum.
shrinkage_calibration: Max-Stein calibration. The default "inverse_moment" uses the reciprocal bootstrap inverse second moment. "second_moment" retains the legacy bootstrap second-moment rule.
gaussian_draws: Optional reusable n by bootstrap_B matrix for the conditional-Gaussian exact-null calibration.
full_endpoint: Definition of the full-model endpoint. The default "thresholded_partial_debiased" preserves the Gaussian-iid framework. "profiled_square_root_lasso" uses the reprofiled partial square-root-LASSO pilot directly and is available for correlated fixed designs. "all_x_square_root_lasso" estimates all p coefficients in one centered-and-scaled square-root-LASSO problem and is the recommended endpoint when FM must use the complete design without an A/B-specific estimation step. Both unthresholded endpoints require test_calibration = "conditional_gaussian".

Value

A maximum-test list with the fitted pilot attached as full_model_beta and full_solver.