practical_power_norm: Find the power of our test for multivariate normal data in a...

In diff-priv-ht/nonpmRegPkg: Implementation of Functions for "Test of Tests"

Find the power of our test for multivariate normal data in a practical setting

Description

Function that finds the parameters, M and theta_0, of our test that yield high power for a given combination of n and epsilon in a practical setting where the effect size is not known and then computes the power at a given effect size.

Usage

practical_power_norm(
  effect_size,
  epsilon,
  n,
  effect_size_grid = seq(0, 1.5, 0.1),
  rho = 0.8,
  alpha = 0.05,
  d = 1,
  n_zeros = 0,
  M_start = min(12, floor(n/3)),
  alpha0_start = 0.2,
  M_max = n
)

Arguments

effect_size	The quotient of the parameter of interest (mu) and the standard deviation of the noise (sigma).
epsilon	The privacy parameter.
n	The number of observations (number of rows in the database).
effect_size_grid	Grid of effect sizes to search over
rho	The desired power threshold
alpha	The significance level. Defaults to 0.05.
d	The number of dimensions (number of columns in the database). Defaults to 1.
n_zeros	The number of entries of the alternative distribution with mean zero. Defaults to 0.
M_start	Starting value of M
alpha0_start	Starting value of alpha0
M_max	The maximum M to search over.

diff-priv-ht/nonpmRegPkg documentation built on Feb. 6, 2023, 5:22 p.m.