dca_M: DCA Algorithm for Upper-Bound Constrained Allocations (M <=...

In stratallo: Optimum Sample Allocation in Stratified Sampling

DCA Algorithm for Upper-Bound Constrained Allocations (M <= N)

Description

Prototype (under testing).

Usage

dca_M(n, H_counts, N, S, rho, rho2, M = N, U = NULL)

Arguments

n	(integerish(1)) total sample size n. Must satisfy ⁠0 < n <= sum(N)⁠.
H_counts	(integerish) strata counts in each domain.
N	(integerish) strata sizes (N_{d,h},\, (d,h) \in \mathcal H).
S	(numeric) standard deviations (S_{d,h},\, (d,h) \in \mathcal H) of surveyed variable in strata.
rho	(numeric) parameters (\rho_d,\, d \in \mathcal D) of the optimization problem.
rho2	(numeric) the square of rho (rho^2), provided to reduce potential loss of precision due to finite-precision arithmetic.
M	(integerish) upper bounds on sample sizes in strata. Defaults to N.
U	(integerish or NULL) a vector of indices identifying the take-max strata, i.e., the strata (d,h) for which the allocation is fixed to x_{d,h} = N_{d,h}. The indices refer to the positions of strata in the set \mathcal H, in the same order as in the input vectors (N, S, etc.). For example, if \mathcal H = \{(1,1),\, (2,1)\} and stratum (2,1) is a take-max stratum, then U = 2. If U contains all strata from a domain, the dimension of the D matrix is reduced accordingly. U must satisfy one of the following conditions: n > sum(N[U]), n = sum(N[U]) and n = sum(N).

Examples

H_counts <- c(5, 2)
H_names <- rep(seq_along(H_counts), times = H_counts)
S <- c(154, 178, 134, 213, 124, 102, 12)
N <- c(100, 100, 100, 100, 100, 100, 100)
M <- c(80, 90, 70, 40, 10, 90, 100)
names(M) <- names(N) <- H_names
total <- c(13, 2)
kappa <- c(0.8, 0.2)
n <- 150

# experimental function (not exported) – examples skipped
## Not run: 
dca_M(n, H_counts, N, S, total, kappa, M = M, U = 5)
#         1         1         1         1         1         2         2
# 12.754880 14.742653 11.098402 17.641490 10.000000 74.945462  8.817113

## End(Not run)

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