CovHT {Frames2}

Covariance estimator between two Horvitz - Thompson estimators

Description

Computes the covariance estimator between two Horvitz - Thompson estimators of population total from survey data obtained from a single stage sampling design

Usage

CovHT(y, x, pikl)

Arguments

y

A numeric vector of size n containing information about first variable of interest in the sample

x

A numeric vector of size n containing information about second variable of interest in the sample

pikl

A square numeric matrix of dimension n containing first and second order inclusion probabilities for units included in the sample

Details

Covariance estimator between two Horvitz - Thompson estimators of population total is given by

\hat{Cov}(\hat{Y}_{HT}, \hat{X}_{HT}) = \sum_{k \in s}\sum_{l \in s} \frac{\pi_{kl} - \pi_k \pi_l}{\pi_{kl}}\frac{y_k}{\pi_k}\frac{x_l}{\pi_l}

Value

A numeric value representing covariance estimator between two Horvitz - Thompson estimators for population total for considered values

References

Horvitz, D. G. and Thompson, D. J. (1952) A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47, 663 - 685 @references Sarndal, C. E., Swensson, B. and Wretman, J. (1992) Model Assisted Survey Sampling. Springer-Verlag. New York.

See Also

HT VarHT

Examples

##########   Example 1   ##########
Indicators <- c(1, 2, 3, 4, 5)
X <- c(13, 18, 20, 14, 9)
Y <- c(2, 0.5, 1.2, 3.3, 2)
#Let draw two simple random samples without replacement of size 2
s <- sample(Indicators, 2)
sX <- X[s]
sY <- Y[s]
#Now, let calculate the associated probability matrix with first and
#second order inclusion probabilities
Ps <- matrix(c(0.4,0.2, 0.2,0.4), 2, 2)
CovHT(sX, sY, Ps)

##########   Example 2   ##########
data(DatA)
attach(DatA)
data(PiklA)
#Let calculate Horvitz - Thompson estimator for total of variable Clothing in Frame A.
HT(Clo, ProbA)
#Let calculate Horvitz - Thompson estimator for total of variable Feeding in Frame A.
HT(Feed, ProbA)
#And now, let compute the covariance between the previous estimators
CovHT(Clo, Feed, PiklA)