PosiR (version 0.1.2)

simultaneous_ci: Compute Simultaneous Confidence Intervals via Bootstrap (Post-Selection Inference)

Description

Implements Algorithm 1 from the reference paper using bootstrap-based max-t statistics to construct valid simultaneous confidence intervals for selected regression coefficients across a user-specified universe of linear models.

Usage

simultaneous_ci(
  X,
  y,
  Q_universe,
  alpha = 0.05,
  B = 1000,
  add_intercept = TRUE,
  bootstrap_method = "pairs",
  cores = 1,
  use_pbapply = TRUE,
  seed = NULL,
  verbose = TRUE,
  ...
)

Value

A list of class simultaneous_ci_result with elements:

• intervals: Data frame with estimates, confidence intervals, variances, and SEs

• K_alpha: Bootstrap (1 - alpha) quantile of max-t statistics

• T_star_b: Vector of bootstrap max-t statistics

• n_valid_T_star_b: Number of finite bootstrap max-t statistics

• alpha, B, bootstrap_method: Metadata

• warnings_list: Internal warnings collected during bootstrap/model fitting

• valid_bootstrap_counts: Valid bootstrap replicates per parameter

• n_bootstrap_errors: Total bootstrap fitting errors

Arguments

X

Numeric matrix (n x p): Design matrix. Must have unique column names. Do not include an intercept if add_intercept = TRUE.

y

Numeric vector (length n): Response vector.

Q_universe

Named list of numeric vectors. Each element specifies a model as a vector of column indices (accounting for intercept if add_intercept = TRUE). Names are used to identify each model in results.

alpha

Significance level for the confidence intervals. Default is 0.05.

B

Integer. Number of bootstrap samples. Default is 1000.

add_intercept

Logical. If TRUE, adds an intercept as the first column of the design matrix. Default is TRUE.

bootstrap_method

Character. Bootstrap type. Only "pairs" is currently supported.

cores

Integer. Number of CPU cores to use for bootstrap parallelization. Default is 1.

use_pbapply

Logical. Use pbapply for progress bars if available. Default is TRUE.

seed

Optional numeric. Random seed for reproducibility. Used for parallel-safe RNG.

verbose

Logical. Whether to display status messages. Default is TRUE.

...

Reserved for future use.

Details

Supports parallel execution, internal warnings capture, and returns structured results with estimates, intervals, bootstrap diagnostics, and inference statistics.

References

Kuchibhotla, A., Kolassa, J., & Kuffner, T. (2022). Post-selection inference. Annual Review of Statistics and Its Application, 9(1), 505–527.

Examples

set.seed(123)
X <- matrix(rnorm(100 * 2), 100, 2, dimnames = list(NULL, c("X1", "X2")))
y <- X[,1] * 0.5 + rnorm(100)
Q <- list(model = 1:2)
res <- simultaneous_ci(X, y, Q, B = 100, cores = 1)
print(res$intervals)
plot(res)