Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the Horvitz-Thompson estimator of the population total according to a *π*PS sampling design

1 |

`y` |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |

`Pik` |
Vector of inclusion probabilities for each unit in the selected sample |

Returns the estimation of the population total of every single variable of interest, its estimated variance and its estimated coefficient of variation under a *π*PPS sampling design. This function uses the results of approximate expressions for
the estimated variance of the Horvitz-Thompson estimator

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

Hugo Andres Gutierrez Rojas hagutierrezro@gmail.com

Matei, A. and Tille, Y. (2005), Evaluation of Variance Approximations and Estimators in Maximun
Entropy Sampling with Unequal Probability and Fixed Sample Design. *Journal of Official Statistics*. Vol 21, 4, 543-570.

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.

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# Uses the Lucy data to draw a sample according to a piPS
# without replacement design
data(Lucy)
attach(Lucy)
# The inclusion probability of each unit is proportional to the variable Income
# The selected sample of size n=400
n <- 400
res <- S.piPS(n, Income)
sam <- res[,1]
# The information about the units in the sample is stored in an object called data
data <- Lucy[sam,]
attach(data)
names(data)
# Pik.s is the inclusion probability of every single unit in the selected sample
Pik.s <- res[,2]
# 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.piPS(estima,Pik.s)
# Same results than HT function
HT(estima, Pik.s)
``` |

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