One-arm distribution-free variance confidence bounds for outcomes in
[0, 1].
Usage
variance_bounds_maurer_pontil(y, beta_l, beta_u, na.rm = TRUE)
variance_bounds_martinez_taboada_ramdas(
y,
beta_l,
beta_u,
na.rm = TRUE,
lower_alpha_split = 0.5,
c1 = 0.5,
c2 = 0.25^2,
c3 = 0.25,
c4 = 0.5,
c5 = 2,
cs = FALSE,
tilde_cs = TRUE
)Arguments
- y
Pilot outcomes for one arm.
- beta_l
One-sided endpoint error for the lower variance bound.
- beta_u
One-sided endpoint error for the upper variance bound.
- na.rm
If
TRUE, drop missing outcomes.- lower_alpha_split
MTR split of the lower-tail error between variance and mean components.
- c1, c2, c3, c4, c5
Martinez-Taboada–Ramdas tuning constants.
- cs, tilde_cs
Logical flags for the MTR predictable-mixture variants.
Value
A list with lower bound L, upper bound U, sample variance vhat, method
name, arm sample size n, and method-specific statistic details. For
Maurer–Pontil bounds, vhat is the raw Bessel sample variance and can
slightly exceed 0.25 in finite samples even though the returned endpoints
are capped to [0, 0.25]; use statistic$projected_vhat for diagnostics
that require a variance on the unit-interval scale.
See also
Other rectangle helpers:
binary_rectangle_corners(),
cmr_multiarm_from_rectangle(),
cmr_stratified_from_rectangle(),
cmr_unbounded_from_rectangle(),
folded_binomial_pmf(),
multiarm_variance_objective(),
rectangle_bernoulli_binary(),
rectangle_bounded_two_arm(),
rectangle_multiarm(),
rectangle_multiple_outcomes(),
rectangle_proxy(),
rectangle_stratified(),
rectangle_unbounded(),
stratified_variance_objective(),
variance_bounds_bernoulli_exact(),
variance_bounds_unbounded_mom()
Examples
y <- c(0.10, 0.30, 0.40, 0.20, 0.70, 0.50)
variance_bounds_maurer_pontil(y, beta_l = 0.025, beta_u = 0.025)
#> $L
#> [1] 0
#>
#> $U
#> [1] 0.25
#>
#> $vhat
#> [1] 0.04666667
#>
#> $method
#> [1] "bounded"
#>
#> $n
#> [1] 6
#>
#> $statistic
#> $statistic$vhat
#> [1] 0.04666667
#>
#> $statistic$projected_vhat
#> [1] 0.04666667
#>
#> $statistic$sdhat
#> [1] 0.2160247
#>
#> $statistic$beta_l
#> [1] 0.025
#>
#> $statistic$beta_u
#> [1] 0.025
#>
#>