Variance-Covariance Matrix of the Sample Membership Indicators for Fixed Size Without Replacement Sampling Designs
Computes the Variance-Covariance matrix of the sample membership indicators in the population given a fixed sample size design
Deltakl(N, n, p)
N |
Population size |
n |
Sample size |
p |
A vector containing the selection probabilities of a fixed size without replacement sampling design. The sum of the values of this vector must be one |
The klth unit of the Variance-Covariance matrix of the sample membership indicators is defined as Δ_{kl}=π_{kl}-π_kπ_l
The function returns a symmetric matrix of size N \times N containing the variances-covariances among the sample membership indicators for each pair of units in the finite population.
Hugo Andres Gutierrez Rojas hagutierrezro@gmail.com
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Vector U contains the label of a population of size N=5
U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie")
N <- length(U)
# The sample size is n=2
n <- 2
# p is the probability of selection of every sample.
p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08)
# Note that the sum of the elements of this vector is one
sum(p)
# Computation of the Variance-Covariance matrix of the sample membership indicators
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