# The Hansen-Hurwitz Estimator Computes the Hansen-Hurwitz Estimator estimator of the population total for several variables of interest ```r 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 ## See Also `HT` ## 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 $i$th unit, and $p_i$ is its corresponding selection probability. This estimator is restricted to with replacement sampling designs. ## Returns 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. ## Examples ```r ############ ## 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) ```

HH.rd function