kStepMAlgorithm function

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.

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.

Returns

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.

Examples

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

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.