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Two-arm variance objectives and Neyman allocation

Source: R/core_variance.R
variance_objective.Rd

Helper functions for the two-arm variance objective, oracle variance, Neyman allocation, and regret. These are useful for checking CMR certificates and comparing CMR against oracle or feasible-Neyman benchmarks.

Usage

variance_objective(pi, v1, v0)

oracle_variance(v1, v0)

assign_neyman(v1, v0)

regret(pi, v1, v0)

Arguments

pi

Treatment assignment share. Values must lie in [0, 1].

v1

Treatment-arm outcome variance. For bounded or Bernoulli outcomes, this must lie in [0, 1/4].

v0

Control-arm outcome variance. For bounded or Bernoulli outcomes, this must lie in [0, 1/4].

Value

Numeric vector after ordinary R recycling of pi, v1, and v0. variance_objective() returns v1 / pi + v0 / (1 - pi), oracle_variance() returns the Neyman-oracle value (sqrt(v1) + sqrt(v0))^2, assign_neyman() returns the treatment share, and regret() returns excess variance relative to the oracle.

See also

Other assignment helpers: assign_balance(), multiarm_variance_objective(), realize_allocation(), stratified_variance_objective()

Examples

v1 <- 0.12
v0 <- 0.04
pi <- assign_neyman(v1, v0)
variance_objective(pi, v1, v0)
#> [1] 0.2985641
oracle_variance(v1, v0)
#> [1] 0.2985641
regret(0.5, v1, v0)
#> [1] 0.02143594