HH: The Hansen-Hurwitz Estimator
In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Computes the Hansen-Hurwitz Estimator estimator of the population total for several variables of interest
Usage
1
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
∑_{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 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.
See Also
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
############
## 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)
Example output
[1] "Yves" "Ken"
[1] 32 34
[1] 1 1
y1 y2
[1,] 32 1
[2,] 34 1
y
Estimation 121.26984
Standard Error 29.84127
CVE 24.60733
y
Estimation 3.6507937
Standard Error 0.7936508
CVE 21.7391304
y1 y2
Estimation 121.26984 3.6507937
Standard Error 29.84127 0.7936508
CVE 24.60733 21.7391304
The following objects are masked from Lucy:
Employees, ID, Income, Level, SPAM, Taxes, Ubication, Zone
[1] "ID" "Ubication" "Level" "Zone" "Income" "Employees"
[7] "Taxes" "SPAM"
Income Employees Taxes
Estimation 1.000504e+06 1.509720e+05 26403.920000
Standard Error 3.029855e+04 3.920522e+03 1870.872910
CVE 3.028329e+00 2.596855e+00 7.085588
[1] 0.122500 0.157500 0.122500 0.087500 0.087500 0.050625 0.078750 0.056250
[9] 0.056250 0.030625 0.043750 0.043750 0.015625 0.031250 0.015625
[1] 1
[,1] [,2] [,3] [,4] [,5]
[1,] 2 0 0 0 0
[2,] 1 1 0 0 0
[3,] 1 0 1 0 0
[4,] 1 0 0 1 0
[5,] 1 0 0 0 1
[6,] 0 2 0 0 0
[7,] 0 1 1 0 0
[8,] 0 1 0 1 0
[9,] 0 1 0 0 1
[10,] 0 0 2 0 0
[11,] 0 0 1 1 0
[12,] 0 0 1 0 1
[13,] 0 0 0 2 0
[14,] 0 0 0 1 1
[15,] 0 0 0 0 2
Warning message:
In if (ID == FALSE) { :
the condition has length > 1 and only the first element will be used
[,1] [,2]
[1,] 32 32
[2,] 32 34
[3,] 32 46
[4,] 32 89
[5,] 32 35
[6,] 34 34
[7,] 34 46
[8,] 34 89
[9,] 34 35
[10,] 46 46
[11,] 46 89
[12,] 46 35
[13,] 89 89
[14,] 89 35
[15,] 35 35
Warning message:
In if (ID == FALSE) { :
the condition has length > 1 and only the first element will be used
[,1] [,2]
[1,] 0.350 0.350
[2,] 0.350 0.225
[3,] 0.350 0.175
[4,] 0.350 0.125
[5,] 0.350 0.125
[6,] 0.225 0.225
[7,] 0.225 0.175
[8,] 0.225 0.125
[9,] 0.225 0.125
[10,] 0.175 0.175
[11,] 0.175 0.125
[12,] 0.175 0.125
[13,] 0.125 0.125
[14,] 0.125 0.125
[15,] 0.125 0.125
[1] 91.42857 121.26984 177.14286 401.71429 185.71429 151.11111 206.98413
[8] 431.55556 215.55556 262.85714 487.42857 271.42857 712.00000 496.00000
[15] 280.00000
X1 X2 X3 X4 X5 Est p
1 2 0 0 0 0 91.42857 0.122500
2 1 1 0 0 0 121.26984 0.157500
3 1 0 1 0 0 177.14286 0.122500
4 1 0 0 1 0 401.71429 0.087500
5 1 0 0 0 1 185.71429 0.087500
6 0 2 0 0 0 151.11111 0.050625
7 0 1 1 0 0 206.98413 0.078750
8 0 1 0 1 0 431.55556 0.056250
9 0 1 0 0 1 215.55556 0.056250
10 0 0 2 0 0 262.85714 0.030625
11 0 0 1 1 0 487.42857 0.043750
12 0 0 1 0 1 271.42857 0.043750
13 0 0 0 2 0 712.00000 0.015625
14 0 0 0 1 1 496.00000 0.031250
15 0 0 0 0 2 280.00000 0.015625
[1] 236
[1] 236
TeachingSampling documentation built on April 22, 2020, 1:05 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Computes the Hansen-Hurwitz Estimator estimator of the population total for several variables of interest
Usage
1 | 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
∑_{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 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.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 | ############
## 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)
|
Example output
[1] "Yves" "Ken"
[1] 32 34
[1] 1 1
y1 y2
[1,] 32 1
[2,] 34 1
y
Estimation 121.26984
Standard Error 29.84127
CVE 24.60733
y
Estimation 3.6507937
Standard Error 0.7936508
CVE 21.7391304
y1 y2
Estimation 121.26984 3.6507937
Standard Error 29.84127 0.7936508
CVE 24.60733 21.7391304
The following objects are masked from Lucy:
Employees, ID, Income, Level, SPAM, Taxes, Ubication, Zone
[1] "ID" "Ubication" "Level" "Zone" "Income" "Employees"
[7] "Taxes" "SPAM"
Income Employees Taxes
Estimation 1.000504e+06 1.509720e+05 26403.920000
Standard Error 3.029855e+04 3.920522e+03 1870.872910
CVE 3.028329e+00 2.596855e+00 7.085588
[1] 0.122500 0.157500 0.122500 0.087500 0.087500 0.050625 0.078750 0.056250
[9] 0.056250 0.030625 0.043750 0.043750 0.015625 0.031250 0.015625
[1] 1
[,1] [,2] [,3] [,4] [,5]
[1,] 2 0 0 0 0
[2,] 1 1 0 0 0
[3,] 1 0 1 0 0
[4,] 1 0 0 1 0
[5,] 1 0 0 0 1
[6,] 0 2 0 0 0
[7,] 0 1 1 0 0
[8,] 0 1 0 1 0
[9,] 0 1 0 0 1
[10,] 0 0 2 0 0
[11,] 0 0 1 1 0
[12,] 0 0 1 0 1
[13,] 0 0 0 2 0
[14,] 0 0 0 1 1
[15,] 0 0 0 0 2
Warning message:
In if (ID == FALSE) { :
the condition has length > 1 and only the first element will be used
[,1] [,2]
[1,] 32 32
[2,] 32 34
[3,] 32 46
[4,] 32 89
[5,] 32 35
[6,] 34 34
[7,] 34 46
[8,] 34 89
[9,] 34 35
[10,] 46 46
[11,] 46 89
[12,] 46 35
[13,] 89 89
[14,] 89 35
[15,] 35 35
Warning message:
In if (ID == FALSE) { :
the condition has length > 1 and only the first element will be used
[,1] [,2]
[1,] 0.350 0.350
[2,] 0.350 0.225
[3,] 0.350 0.175
[4,] 0.350 0.125
[5,] 0.350 0.125
[6,] 0.225 0.225
[7,] 0.225 0.175
[8,] 0.225 0.125
[9,] 0.225 0.125
[10,] 0.175 0.175
[11,] 0.175 0.125
[12,] 0.175 0.125
[13,] 0.125 0.125
[14,] 0.125 0.125
[15,] 0.125 0.125
[1] 91.42857 121.26984 177.14286 401.71429 185.71429 151.11111 206.98413
[8] 431.55556 215.55556 262.85714 487.42857 271.42857 712.00000 496.00000
[15] 280.00000
X1 X2 X3 X4 X5 Est p
1 2 0 0 0 0 91.42857 0.122500
2 1 1 0 0 0 121.26984 0.157500
3 1 0 1 0 0 177.14286 0.122500
4 1 0 0 1 0 401.71429 0.087500
5 1 0 0 0 1 185.71429 0.087500
6 0 2 0 0 0 151.11111 0.050625
7 0 1 1 0 0 206.98413 0.078750
8 0 1 0 1 0 431.55556 0.056250
9 0 1 0 0 1 215.55556 0.056250
10 0 0 2 0 0 262.85714 0.030625
11 0 0 1 1 0 487.42857 0.043750
12 0 0 1 0 1 271.42857 0.043750
13 0 0 0 2 0 712.00000 0.015625
14 0 0 0 1 1 496.00000 0.031250
15 0 0 0 0 2 280.00000 0.015625
[1] 236
[1] 236
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.