HH {TeachingSampling}

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 containing the recollected information of the variables of interest for every unit in the selected sample

pk

A vector containing selection probabilities for each unit in the selected sample

Details

The Hansen-Hurwitz estimator is given by

\sum_{i=1}^m\frac{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 vector of total population estimates for each variable of interest, its estimated standard error and its estimated coefficient of variation.

Author(s)

Hugo Andres Gutierrez Rojas [e-mail]

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.

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(0.35, 0.225, 0.175, 0.125, 0.125)
# 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 Lucy data to draw a simple random sample with replacement
data(Lucy)
attach(Lucy)

N <- dim(Lucy)[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)

################################################################
## Example 3 HH is unbiased for with replacement sampling designs
################################################################

# 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
y<-c(32, 34, 46, 89, 35)
# 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(0.35, 0.225, 0.175, 0.125, 0.125)
# p is the probability of selection of every possible sample
p <- p.WR(N,m,pk)
p
sum(p)
# The sample membership matrix for random size without replacement sampling designs
Ind <- nk(N,m)
Ind
# The support with the values of the elements
Qy <- SupportWR(N,m, ID=y)                 
Qy
# The support with the values of the elements
Qp <- SupportWR(N,m, ID=pk)                 
Qp
# The HT estimates for every single sample in the support
HH1 <- HH(Qy[1,], Qp[1,])[1,]
HH2 <- HH(Qy[2,], Qp[2,])[1,]
HH3 <- HH(Qy[3,], Qp[3,])[1,] 
HH4 <- HH(Qy[4,], Qp[4,])[1,] 
HH5 <- HH(Qy[5,], Qp[5,])[1,] 
HH6 <- HH(Qy[6,], Qp[6,])[1,] 
HH7 <- HH(Qy[7,], Qp[7,])[1,]
HH8 <- HH(Qy[8,], Qp[8,])[1,]
HH9 <- HH(Qy[9,], Qp[9,])[1,]
HH10 <- HH(Qy[10,], Qp[10,])[1,]
HH11 <- HH(Qy[11,], Qp[11,])[1,]
HH12 <- HH(Qy[12,], Qp[12,])[1,]
HH13 <- HH(Qy[13,], Qp[13,])[1,]
HH14 <- HH(Qy[14,], Qp[14,])[1,]
HH15 <- HH(Qy[15,], Qp[15,])[1,]
# The HT estimates arranged in a vector
Est <- c(HH1, HH2, HH3, HH4, HH5, HH6, HH7, HH8, HH9, HH10, HH11, HH12, HH13,
HH14, HH15)
Est
# The HT is actually desgn-unbiased
data.frame(Ind, Est, p)
sum(Est*p)
sum(y)