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Unbounded-outcome median-of-means variance bounds

Source: R/cmr_unbounded.R
variance_bounds_unbounded_mom.Rd

Compute one-arm median-of-means variance bounds for raw numeric outcomes under a bounded-kurtosis input psi.

Usage

variance_bounds_unbounded_mom(y, alpha = 0.05, psi = NULL, na.rm = TRUE)

Arguments

y

One-arm pilot outcomes.

alpha

Error budget used to size the number of blocks, k = ceiling(8 * log(2 / alpha)). The resulting one-arm two-sided coverage error is at most alpha / 2, so that two arms sized with the same alpha jointly satisfy the union bound at level alpha, as consumed by rectangle_unbounded().

psi

Bounded-kurtosis parameter. Must be at least 1.

na.rm

If TRUE, drop missing outcomes.

Value

A list with lower bound L, upper bound U, median-of-means variance estimate vhat, method name, sample size n, activation flag active, status string, and block-level statistic details. If the pilot is too small or the relative-error radius is too large, active = FALSE, L = NA, and U = Inf.

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_maurer_pontil()

Examples

set.seed(2)
y <- rnorm(2000, sd = 1.3)
variance_bounds_unbounded_mom(y, alpha = 0.05, psi = 3)
#> $L
#> [1] 1.173903
#> 
#> $U
#> [1] 3.451095
#> 
#> $vhat
#> [1] 1.751893
#> 
#> $method
#> [1] "unbounded_mom"
#> 
#> $n
#> [1] 2000
#> 
#> $active
#> [1] TRUE
#> 
#> $status
#> [1] "active"
#> 
#> $statistic
#> $statistic$alpha
#> [1] 0.05
#> 
#> $statistic$psi
#> [1] 3
#> 
#> $statistic$k
#> [1] 30
#> 
#> $statistic$b
#> [1] 33
#> 
#> $statistic$n_pairs
#> [1] 1000
#> 
#> $statistic$used_pairs
#> [1] 990
#> 
#> $statistic$discarded_pairs
#> [1] 10
#> 
#> $statistic$rho
#> [1] 0.492366
#> 
#> $statistic$vhat
#> [1] 1.751893
#> 
#> $statistic$block_means
#>  block_1  block_2  block_3  block_4  block_5  block_6  block_7  block_8 
#> 2.518868 1.637589 1.886652 2.212851 1.577163 1.346077 1.776847 1.818456 
#>  block_9 block_10 block_11 block_12 block_13 block_14 block_15 block_16 
#> 1.947647 1.414576 2.153929 1.210690 1.949323 1.307376 1.673664 1.305325 
#> block_17 block_18 block_19 block_20 block_21 block_22 block_23 block_24 
#> 1.353364 2.259950 1.856922 1.961559 2.038161 1.452617 1.246178 1.200749 
#> block_25 block_26 block_27 block_28 block_29 block_30 
#> 1.729985 1.773801 1.813644 1.786194 1.418878 1.366431 
#> 
#>