rnabox: Recursive Neyman Algorithm for Optimum Sample Allocation...
In stratallo: Optimum Sample Allocation in Stratified Sampling

rnabox

R Documentation

Recursive Neyman Algorithm for Optimum Sample Allocation under Box Constraints (RNABOX)

Description

Implements the Recursive Neyman Algorithm for Optimum Sample Allocation under Box Constraints (RNABOX), as proposed in \insertCiternabox;textualstratallo. The algorithm solves the following optimum allocation problem, formulated in mathematical optimization terms:

Minimize

f(x_1,\ldots,x_H) = \sum_{h=1}^H \frac{A^2_h}{x_h}

over \mathbb R_+^H, subject to

\sum_{h=1}^H x_h = n,

m_h \leq x_h \leq M_h, \qquad h = 1,\ldots,H,

where n > 0,\, A_h > 0,\, m_h > 0,\, M_h > 0, such that m_h < M_h,\, h = 1,\ldots,H, and \sum_{h=1}^H m_h \leq n \leq \sum_{h=1}^H M_h, are given numbers. Inequality constraints are optional and may be omitted.

Usage

rnabox(
  n,
  A,
  bounds_inner = NULL,
  bounds_outer = NULL,
  cmp_inner = .Primitive(">="),
  cmp_outer = .Primitive("<=")
)

Arguments

`n`	(`integerish(1)`) total sample size. Must satisfy `n > 0`. Additionally: If `bounds_inner` is not `NULL`, then `n >= sum(bounds_inner)` when `bounds_inner` are treated as lower bounds, or `n <= sum(bounds_inner)` when treated as upper bounds. If `bounds_outer` is not `NULL`, then `n >= sum(bounds_outer)` when `bounds_outer` are treated as lower bounds, or `n <= sum(bounds_outer)` when treated as upper bounds.
`A`	(`numeric`) population constants `A_1,\ldots,A_H`. All values must be strictly positive.
`bounds_inner`	(`numeric` or `NULL`) optional bounds on sample sizes in strata for the interim (inner) allocation phase of `rnabox()`. These can be either lower bounds `m_1,\ldots,m_H` or upper bounds `M_1,\ldots,M_H`, depending on the value of `cmp_inner`. If `bounds_inner` is `NULL`, no bounds are imposed during the interim allocation phase. If both `bounds_inner` and `bounds_outer` are not `NULL`, the following element-wise relationships must hold: If `bounds_inner` are treated as lower bounds, then `bounds_inner < bounds_outer`. If `bounds_inner` are treated as upper bounds, then `bounds_inner > bounds_outer`. `bounds_inner` is passed by `rnabox()` to `rna()` as the `bounds` argument, serving as an interim allocation step applied before enforcing the outer `bounds_outer`.
`bounds_outer`	(`numeric` or `NULL`) optional bounds on sample sizes in strata, checked during the violation check (outer) phase of the iterative `rnabox()` loop. These can be either lower bounds `m_1,\ldots,m_H` or upper bounds `M_1,\ldots,M_H`, depending on the value of `cmp_outer`. If `bounds_outer` is `NULL`, no bounds are imposed during the outer phase. If both `bounds_outer` and `bounds_inner` are not `NULL`, the following element-wise relationships must hold: If `bounds_outer` are treated as lower bounds, then `bounds_outer < bounds_inner`. If `bounds_outer` are treated as upper bounds, then `bounds_outer > bounds_inner`.
`cmp_inner`	(`function`) a binary comparison operator used to check for violations of `bounds_inner`. Must be either `.Primitive("<=")` or `.Primitive(">=")`. This operator determines how `bounds_inner` is handled: `.Primitive("<=")` treats `bounds_inner` as lower bounds and causes `rnabox()` to apply the LRNA algorithm as an inner allocation step. `.Primitive(">=")` treats `bounds_inner` as upper bounds and causes `rnabox()` to apply the RNA algorithm as an inner allocation step. The value of this argument has no effect if `bounds_inner` is `NULL`. `cmp_inner` is passed by `rnabox()` to `rna()` as the `cmp` argument, serving as an interim allocation step applied before enforcing the outer `bounds_outer`.
`cmp_outer`	(`function`) a binary comparison operator used to check for violations of `bounds_outer`. It must be the logical complement of `cmp_inner` (up to equality): if `cmp_inner = .Primitive("<=")`, then `cmp_outer = .Primitive(">=")`, and vice versa. It determines how `bounds_outer` is handled: `.Primitive("<=")` treats `bounds_outer` as lower bounds. `.Primitive(">=")` treats `bounds_outer` as upper bounds. The value of this argument has no effect if `bounds_outer` is `NULL`. `cmp_outer` is provided solely for computational efficiency, as its value is fully determined by `cmp_inner`.

Value

A numeric vector of optimum sample allocations in strata.

Note

The rnabox() function is optimized for internal use and should typically not be called directly by users. Use opt() instead.

References

\insertRef

rnaboxstratallo

Examples

N <- c(454, 10, 116, 2500, 2240, 260, 39, 3000, 2500, 400)
S <- c(0.9, 5000, 32, 0.1, 3, 5, 300, 13, 20, 7)
A <- N * S
m <- c(322, 3, 57, 207, 715, 121, 9, 1246, 1095, 294) # lower bounds
M <- N # upper bounds

# Regular allocation.
n <- 6000
opt_regular <- rnabox(n, A, M, m)

# Vertex allocation.
n <- 4076
opt_vertex <- rnabox(n, A, M, m)

stratallo documentation built on March 12, 2026, 5:06 p.m.