Compute the design Mean Squared Error of five sampling strategies.
Usage
desmse(y, x, n, H, d2, d4)
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 smaller or equal than length(x) 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.
Value
A vector of length five with the Mean Squared Error of the five sample strategies in the following order: \(\pi\)ps--reg, STSI--reg, STSI--HT, \(\pi\)ps--pos and STSI--pos.
Details
The design Mean Squared Error of a sample of size n is computed for five sampling strategies (\(\pi\)ps--reg, STSI--reg, STSI--HT, \(\pi\)ps--pos and STSI--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
expmse for the anticipated MSE of the five strategies.