BalancedSampling (version 2.0.6)

cube: The Cube method

Description

Selects balanced samples with prescribed inclusion probabilities from a finite population using the fast flight Cube Method.

Usage

cube(prob, x, eps = 1e-12)
cubestratified(prob, x, integerStrata, eps = 1e-12)

Value

A vector of selected indices in 1,2,...,N.

Arguments

prob

A vector of length N with inclusion probabilities.

x

An N by q matrix of balancing auxiliary variables.

eps

A small value used to determine when an updated probability is close enough to 0.0 or 1.0.

integerStrata

An integer vector of length N with stratum numbers.

Functions

• cubestratified():

Details

If prob sum to an integer n, and prob is included as the first balancing variable, a fixed sized sample (n) will be produced.

Stratified cube

For cubestratified, prob is automatically inserted as a balancing variable.

The stratified version uses the fast flight Cube method and pooling of landing phases.

References

Deville, J. C. and Tillé, Y. (2004). Efficient balanced sampling: the cube method. Biometrika, 91(4), 893-912.

Chauvet, G. and Tillé, Y. (2006). A fast algorithm for balanced sampling. Computational Statistics, 21(1), 53-62.

Chauvet, G. (2009). Stratified balanced sampling. Survey Methodology, 35, 115-119.

See Also

Other sampling: hlpm2(), lcube(), lpm(), scps()

Examples

if (FALSE) {
set.seed(12345);
N = 1000;
n = 100;
prob = rep(n/N, N);
x = matrix(runif(N * 2), ncol = 2);
s = cube(prob, x);
plot(x[, 1], x[, 2]);
points(x[s, 1], x[s, 2], pch = 19);

set.seed(12345);
N = 1000;
n = 100;
prob = rep(n/N, N);
x = matrix(runif(N * 2), ncol = 2);
strata = c(rep(1L, 100), rep(2L, 200), rep(3L, 300), rep(4L, 400));
s = cubestratified(prob, x, strata);
plot(x[, 1], x[, 2]);
points(x[s, 1], x[s, 2], pch = 19);

set.seed(12345);
prob = c(0.2, 0.25, 0.35, 0.4, 0.5, 0.5, 0.55, 0.65, 0.7, 0.9);
N = length(prob);
x = matrix(runif(N * 2), ncol = 2);
ep = rep(0L, N);
r = 10000L;
for (i in seq_len(r)) {
  s = cube(prob, cbind(prob, x));
  ep[s] = ep[s] + 1L;
}
print(ep / r);
}