optimStrat (version 2.4)

desvar: Design variance

Description

Compute the design variance of six sampling strategies.

Usage

desvar(y, x, n, H, d2, d4)

Value

A vector of length six with the variance of the six sampling strategies.

Arguments

y

a numeric vector giving the values of the study variable.

x

a positive numeric vector giving the values of the auxiliary variable.

n

a positive integer indicating the desired sample size.

H

a positive integer giving the desired number of strata/poststrata.

d2

a number giving the assumed shape of the trend term in the superpopulation model.

d4

a number giving the assumed shape of the spread term in the superpopulation model.

Details

The design variance of a sample of size n is computed for six sampling strategies (stsi--HT, \(\pi\)ps--HT, stsi--pos, \(\pi\)ps--pos, stsi--reg and \(\pi\)ps--pos). The strategies are defined assuming that there is an underlying superpopulation model of the form $$Y_{k}=\delta_{0}+\delta_{1}x_{k}^{\delta_{2}}+\epsilon_{k}$$ with \(E\epsilon_{k}=0\), \(V\epsilon_{k}=\delta_{3}^{2}x_{k}^{2\delta_{4}}\) and \(Cov(\epsilon_{k},\epsilon_{l})=0\).

The number of strata/poststrata is given by H.

References

Bueno, E. (2018). A Comparison of Stratified Simple Random Sampling and Probability Proporional-to-size Sampling. Research Report, Department of Statistics, Stockholm University 2018:6. http://gauss.stat.su.se/rr/RR2018_6.pdf.

See Also

expvar for the expected variance of five sampling strategies.

Examples

f<- function(x,b0,b1,b2,...) {b0+b1*x^b2}
g<- function(x,b3,...) {x^b3}
x<- 1 + sort( rgamma(5000, shape=4/9, scale=108) )
y<- simulatey(x,f,g,dist="gamma",b0=10,b1=1,b2=1.25,b3=0.5,rho=0.90)

desvar(y,x,n=500,H=6,d2=1.25,d4=0.50)
desvar(y,x,n=500,H=6,d2=1.00,d4=1.00)