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

rnabox

R Documentation

Recursive Neyman Algorithm for Optimal Sample Allocation Under Box Constraints

Description

An internal function that implements the RNABOX algorithm that solves the following optimal allocation problem, formulated below in the language of mathematical optimization.

Minimize

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

subject to

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

m_h \leq x_h \leq M_h, \quad 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. The minimization is on \mathbb R_+^H. Inequality constraints are optional and can be skipped.

rnabox() function should not be called directly by the user. Use opt() instead.

Usage

rnabox(
  n,
  A,
  bounds1 = NULL,
  bounds2 = NULL,
  check_violations1 = .Primitive(">="),
  check_violations2 = .Primitive("<=")
)

Arguments

`n`	(`number`) total sample size. A strictly positive scalar. If `bounds1` is not `NULL`, it is then required that `n >= sum(bounds1)` (given that `bounds1` are treated as lower bounds) or `n <= sum(bounds1)` (given that `bounds1` are treated as upper bounds). If `bounds2` is not `NULL`, it is then required that `n >= sum(bounds2)` (given that `bounds2` are treated as lower bounds) or `n <= sum(bounds2)` (given that `bounds2` are treated as upper bounds).
`A`	(`numeric`) population constants `A_1,\ldots,A_H`. Strictly positive numbers.
`bounds1`	(`numeric` or `NULL`) lower bounds `m_1,\ldots,m_H`, or upper bounds `M_1,\ldots,M_H` optionally imposed on sample sizes in strata. The interpretation of `bounds1` depends on the value of `check_violations1`. If no one-sided bounds 1 should be imposed, then `bounds1` must be set to `NULL`. If `bounds2` is not `NULL`, it is then required that either `bounds1 < bounds2` (in case when `bounds1` is treated as lower bounds) or `bounds1 > bounds2` (in the opposite case).
`bounds2`	(`numeric` or `NULL`) lower bounds `m_1,\ldots,m_H`, or upper bounds `M_1,\ldots,M_H` optionally imposed on sample sizes in strata. The interpretation of `bounds2` depends on the value of `check_violations2`. If no one-sided bounds 2 should be imposed, then `bounds2` must be set to `NULL`. If `bounds2` is not `NULL`, it is then required that either `bounds1 < bounds2` (in case when `bounds1` is treated as lower bounds) or `bounds1 > bounds2` (in the opposite case).
`check_violations1`	(`function`) 2-arguments binary operator function that allows the comparison of values in atomic vectors. It must either be set to `.Primitive("<=")` or `.Primitive(">=")`. The first of these choices causes that `bounds1` are treated as lower bounds and the `rnabox()` uses the LRNA algorithm as in interim algorithm for the allocation problem with one-sided lower bounds `bounds1`. The latter option causes that `bounds1` are treated as upper bounds and the `rnabox()` uses the RNA algorithm as in interim algorithm for the allocation problem with one-sided upper bounds `bounds1`. This parameter is correlated with `check_violations2`. That is, these arguments must be set against each other. `check_violations1` is ignored when `bounds1` is set to `NULL`.
`check_violations2`	(`function`) 2-arguments binary operator function that allows the comparison of values in atomic vectors. It must either be set to `.Primitive("<=")` or `.Primitive(">=")`. The first of these choices causes that `bounds2` are treated as lower bounds and the `rnabox()` uses the LRNA algorithm as in interim algorithm for the allocation problem with one-sided lower bounds `bounds2`. The latter option causes that `bounds2` are treated as upper bounds and the `rnabox()` uses the RNA algorithm as in interim algorithm for the allocation problem with one-sided upper bounds `bounds2`. This parameter is correlated with `check_violations1`. That is, these arguments must be set against each other. `check_violations2` is ignored when `bounds2` is set to `NULL`.

Value

Numeric vector with optimal sample allocations in strata.

References

To be added soon.

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 Nov. 27, 2023, 1:07 a.m.