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CPSS–SM shrinkage toward an all-predictor dual-Ridge endpoint

Source: R/fit-cpss-ridge-shrinkage.R
fit_cpss_ridge_shrinkage.Rd

fit_cpss_ridge_shrinkage() combines an all-X Ridge full-model endpoint with a fresh exact-null SVD submodel endpoint. A conditional-Gaussian maximum partial-t test is calculated from the exact-null residual, not from the biased Ridge estimator. The function returns preliminary-test, Stein-type, positive-part, and pretest-protected positive-part estimators.

Usage

fit_cpss_ridge_shrinkage(
  X,
  y,
  core_set = NULL,
  selection = NULL,
  ridge_lambda = NULL,
  ridge_lambda_grid = NULL,
  selector_label = NULL,
  alpha = 0.05,
  gaussian_draws = NULL,
  bootstrap_B = 999L,
  bootstrap_seed = NULL,
  bootstrap_block_size = 256L,
  rank_tolerance = 1e-10,
  shrinkage_calibration = c("inverse_moment", "second_moment"),
  epsilon = 1e-10
)

Arguments

X

Numeric analysis-sample design matrix.

y

Numeric analysis-sample response.

core_set

One-based selected core indices, or a cpss_core_selection object.

selection

Alternatively, an object returned by cpss_select_core(). Named features are aligned to X by identity.

ridge_lambda

Optional fixed positive Ridge penalty. If omitted, GCV selects from ridge_lambda_grid using the existing all-X dual path.

ridge_lambda_grid

Optional positive GCV grid.

selector_label

Label describing the independently selected core.

alpha

Conditional Monte Carlo test level.

gaussian_draws

Optional reusable n by bootstrap_B matrix of iid standard Gaussian draws.

bootstrap_B

Number of Gaussian draws when gaussian_draws is absent.

bootstrap_seed

Optional reproducible Gaussian-draw seed.

bootstrap_block_size

C++ calibration block size.

rank_tolerance

Relative economy-SVD rank tolerance.

shrinkage_calibration

Null calibration for the max-Stein weight.

epsilon

Positive numerical floor for the squared statistic.

Value

An hd_shrinkage_fit object with FM, SM, PT, S, PS, and PPS endpoints.

References

Shah, R. D. and Samworth, R. J. (2013). Variable selection with error control: another look at stability selection. Journal of the Royal Statistical Society: Series B, 75, 55–80. doi:10.1111/j.1467-9868.2011.01034.x

Dufour, J.-M. (2006). Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and nonstandard asymptotics. Journal of Econometrics, 133, 443–477. doi:10.1016/j.jeconom.2005.06.007

Yuzbasi, B., Arashi, M. and Ahmed, S. E. (2020). Shrinkage estimation strategies in high-dimensional linear models. International Statistical Review. doi:10.1111/insr.12351