# E.SI: Estimation of the Population Total under Simple Random... In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Computes the Horvitz-Thompson estimator of the population total according to an SI sampling design

## Usage

 `1` ```E.SI(N, n, y) ```

## Arguments

 `N` Population size `n` Sample size `y` Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample

## Details

Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation under an SI sampling design

## Value

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

## 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.

`S.SI`
 ``` 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``` ```############ ## Example 1 ############ # Uses the Lucy data to draw a random sample of units according to a SI design data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # 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) E.SI(N,n,estima) ############ ## Example 2 ############ # Following with Example 1. The variable SPAM is a domain of interest Doma <- Domains(SPAM) # This function allows to estimate the size of each domain in SPAM estima <- data.frame(Doma) E.SI(N,n,Doma) ############ ## Example 3 ############ # Following with Example 1. The variable SPAM is a domain of interest Doma <- Domains(SPAM) # This function allows to estimate the parameters of the variables of interest # for every category in the domain SPAM estima <- data.frame(Income, Employees, Taxes) SPAM.no <- cbind(Doma[,1], estima*Doma[,1]) SPAM.yes <- cbind(Doma[,1], estima*Doma[,2]) # Before running the following lines, notice that: # The first column always indicates the population size # The second column is an estimate of the size of the category in the domain SPAM # The remaining columns estimates the parameters of interest # within the corresponding category in the domain SPAM E.SI(N,n,SPAM.no) E.SI(N,n,SPAM.yes) ############ ## Example 4 ############ # Following with Example 1. The variable SPAM is a domain of interest # and the variable ISO is a populational subgroup of interest Doma <- Domains(SPAM) estima <- Domains(Zone) # Before running the following lines, notice that: # The first column indicates wheter the unit # belongs to the first category of SPAM or not # The remaining columns indicates wheter the unit # belogns to the categories of Zone SPAM.no <- data.frame(SpamNO=Doma[,1], Zones=estima*Doma[,1]) # Before running the following lines, notice that: # The first column indicates wheter the unit # belongs to the second category of SPAM or not # The remaining columns indicates wheter the unit # belogns to the categories of Zone SPAM.yes <- data.frame(SpamYES=Doma[,2], Zones=estima*Doma[,2]) # Before running the following lines, notice that: # The first column always indicates the population size # The second column is an estimate of the size of the # first category in the domain SPAM # The remaining columns estimates the size of the categories # of Zone within the corresponding category of SPAM # Finnaly, note that the sum of the point estimates of the last # two columns gives exactly the point estimate in the second column E.SI(N,n,SPAM.no) # Before running the following lines, notice that: # The first column always indicates the population size # The second column is an estimate of the size of the # second category in the domain SPAM # The remaining columns estimates the size of the categories # of Zone within the corresponding category of SPAM # Finnaly, note that the sum of the point estimates of the last two # columns gives exactly the point estimate in the second column E.SI(N,n,SPAM.yes) ```