# VarHT: Variance of the Horvitz-Thompson Estimator In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Computes the theoretical variance of the Horvitz-Thompson estimator given a without replacement fixed sample size design

## Usage

 1 VarHT(y, N, n, p) 

## Arguments

 y Vector containing the recollected information of the characteristic of interest for every unit in the population 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 variance of the Horvitz-Thompson estimator, under a given sampling design p, is given by

Var_p(\hat{t}_{y,π})=∑_{k\in U}∑_{l \in U}Δ_{kl}\frac{y_k}{π_k}\frac{y_l}{π_l}

## Value

The function returns the value of the theoretical variances of the Horviz-Thompson estimator.

## Author(s)

Hugo Andres Gutierrez Rojas hagutierrezro@gmail.com

## 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.

HT, Deltakl, Pikl, Pik

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 # Without replacement sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) # The population size is N=5 N <- length(U) # The sample size is n=2 n <- 2 # p is the probability of selection of every possible sample p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Calculates the theoretical variance of the HT estimator VarHT(y1, N, n, p) VarHT(y2, N, n, p) 

### Example output

[1] 7847.211
[1] 2.342123


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