k-StepM Algorithm for Hypothesis Testing

This function implements the k-stepM algorithm for multiple hypothesis testing. It tests each hypothesis using the critical value calculated from the ECDF of the k-max differences, updating the critical value, and iterating until all hypotheses are tested.

Usage

kStepMAlgorithm(original_stats, bootstrap_stats, num_hypotheses, alpha, k)

Arguments

original_stats

A numeric vector of original test statistics for each hypothesis.

bootstrap_stats

A numeric matrix of bootstrap test statistics, with rows representing bootstrap samples and columns representing hypotheses.

num_hypotheses

An integer specifying the total number of hypotheses.

alpha

A numeric value specifying the significance level.

k

An integer specifying the threshold number for controlling the k-familywise error rate.

Value

A list containing two elements: 'signif', a logical vector indicating which hypotheses are rejected, and 'cv', a numeric vector of critical values used for each hypothesis.

References

Romano, Joseph P., Azeem M. Shaikh, and Michael Wolf. "Formalized data snooping based on generalized error rates." Econometric Theory 24.2 (2008): 404-447.

Examples

original_stats <- rnorm(10)
bootstrap_stats <- matrix(rnorm(1000), ncol = 10)
result <- kStepMAlgorithm(original_stats, bootstrap_stats, 10, 0.05, 1)