# VarHT: Variance estimator of Horvitz - Thompson estimator In Frames2: Estimation in Dual Frame Surveys

## Description

Computes the variance estimator of Horvitz - Thompson estimator of population total

## Usage

 1 VarHT(y, pikl) 

## Arguments

 y A numeric vector of size n containing information about variable of interest pikl A square numeric matrix of dimension n containing first and second order inclusion probabilities for units included in y

## Details

Variance estimator of Horvitz - Thompson estimator of population total is given by

\hat{Var}(\hat{Y}_{HT}) = ∑_{k \in s}\frac{y_k^2}{π_k^2}(1 - π_k) + ∑_{k \in s}∑_{l \in s, l \neq k} \frac{y_k y_l}{π_k π_l} \frac{π_{kl} - π_k π_l}{π_{kl}}

## Value

A numeric value representing variance estimator of Horvitz - Thompson estimator 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

Sarndal, C. E., Swensson, B. and Wretman, J. (1992) Model Assisted Survey Sampling. Springer-Verlag. New York.

HT CovHT
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ########## Example 1 ########## U <- c(13, 18, 20, 14, 9) #A simple random sample of size 2 without replacement is drawn from population s <- sample(U, 2) #Horvitz - Thompson estimator of population total is calculated. ps <- c(0.4, 0.4) HT(s, ps) #Now, we calculate variance estimator of the Horvitz - Thompson estimator. Ps <- matrix(c(0.4,0.1, 0.1,0.4), 2 ,2) VarHT(s, 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) #And now, let compute the variance of the previous estimator VarHT(Clo, PiklA)