Deltakl: Variance-Covariance Matrix of the Sample Membership...

In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

Description

Computes the Variance-Covariance matrix of the sample membership indicators in the population given a fixed sample size design

Usage

Deltakl(N, n, p)

Arguments

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

Details

The klth unit of the Variance-Covariance matrix of the sample membership indicators is defined as Δ_{kl}=π_{kl}-π_kπ_l

Value

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.

Author(s)

Hugo Andres Gutierrez Rojas [e-mail]

References

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.

See Also

VarHT, Pikl, Pik

Examples

# 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
Deltakl(N, n, p)

Example output

[1] 1
        [,1]    [,2]    [,3]    [,4]    [,5]
[1,]  0.2436 -0.0672 -0.0784 -0.0414 -0.0566
[2,] -0.0672  0.2244 -0.0132 -0.0722 -0.0718
[3,] -0.0784 -0.0132  0.2496 -0.0984 -0.0596
[4,] -0.0414 -0.0722 -0.0984  0.2211 -0.0091
[5,] -0.0566 -0.0718 -0.0596 -0.0091  0.1971

TeachingSampling documentation built on April 22, 2020, 1:05 a.m.