HH {TeachingSampling}R Documentation

The Hansen-Hurwitz Estimator

Description

Computes the Hansen-Hurwitz Estimator estimator of the population total for several variables of interest

Usage

HH(y, pk)

Arguments

y Vector, matrix or data frame containig the recollected information of the variables of interest for every unit in the selected sample
pk A vetor containing selection probabilities for each unit in the selected sample

Details

The Hansen-Hurwitz estimator is given by

sum_{i=1}^mfrac{y_i}{p_i}

where y_i is the value of the variables of interest for the ith unit, and p_i is its corresponding selection probability. This estimator is restricted to with replacement sampling designs.

Value

The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest

Author(s)

Hugo Andrés Gutiérrez Rojas hugogutierrez@usantotomas.edu.co

References

Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Guti'errez, H. A. (2009), Estrategias de muestreo: Dise~no de encuestas y estimaci'on de par'ametros. Editorial Universidad Santo Tom'as.

See Also

HT

Examples

############
## Example 1
############
# Vector U contains the label of a population of size N=5
U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie")
# Vectors y1 and y2 give the values of the variables of interest
y1<-c(32, 34, 46, 89, 35)
y2<-c(1,1,1,0,0)
y3<-cbind(y1,y2)
# The population size is N=5
N <- length(U)
# The sample size is m=2
m <- 2
# pk is the probability of selection of every single unit
pk <- c(0.9, 0.025, 0.025, 0.025, 0.025)
# Selection of a random sample with replacement
sam <- sample(5,2, replace=TRUE, prob=pk)
# The selected sample is
U[sam]
# The values of the variables of interest for the units in the sample
y1[sam]
y2[sam]
y3[sam,]
# The Hansen-Hurwitz estimator
HH(y1[sam],pk[sam])
HH(y2[sam],pk[sam])
HH(y3[sam,],pk[sam])

############
## Example 2
############
# Uses the Marco and Lucy data to draw a simple random sample with replacement
data(Marco)
data(Lucy)

N <- dim(Marco)[1]
m <- 400
sam <- sample(N,m,replace=TRUE)
# The vector of selection probabilities of units in the sample
pk <- rep(1/N,m)
# The information about the units in the sample is stored in an object called data
data <- Lucy[sam,]
attach(data)
names(data)
# The variables of interest are: Income, Employees and Taxes
# This information is stored in a data frame called estima
estima <- data.frame(Income, Employees, Taxes)
HH(estima, pk)

[Package TeachingSampling version 0.7.6 Index]