frob_norm_sq_debiased_times_matrix {OptimalRerandExpDesigns}

Debiased Frobenius Norm Squared Constant Times Var-Cov matrix

Description

Compute debiased Frobenius Norm of matrix P times Sigmahat (Appendix 5.9). Note that for S <= 2, it returns the naive estimate.

Usage

frob_norm_sq_debiased_times_matrix(
  Sigmahat,
  A,
  s,
  n,
  frob_norm_sq_bias_correction_min_samples = 10
)

Arguments

Sigmahat

The var-cov matrix of interest

A

The matrix that multiplies Sigmahat

s

The number of vectors Sigmahat was generated from

n

The length of each vector

frob_norm_sq_bias_correction_min_samples

This estimate suffers from high variance when there are not enough samples. Thus, we only implement the correction beginning at this number of samples otherwise we return the naive estimate. Default is 10.

Value

The unbiased estimate of the Frobenius Norm of A times a variance-covariance matrix quantity squared.

Author(s)

Adam Kapelner