Est.Mean.NHT | R Documentation |
Computes the Narain (1951); Horvitz-Thompson (1952) estimator for a population mean.
Est.Mean.NHT(VecY.s, VecPk.s, N)
VecY.s |
vector of the variable of interest; its length is equal to n, the sample size. Its length has to be the same as that of |
VecPk.s |
vector of the first-order inclusion probabilities; its length is equal to n, the sample size. Values in |
N |
the population size. It must be an integer or a double-precision scalar with zero-valued fractional part. |
For the population mean of the variable y:
\bar{y} = \frac{1}{N} ∑_{k\in U} y_k
the unbiased Narain (1951); Horvitz-Thompson (1952) estimator of \bar{y} (implemented by the current function) is given by:
\hat{\bar{y}}_{NHT} = \frac{1}{N} ∑_{k\in s} \frac{y_k}{π_k}
where π_k denotes the inclusion probability of the k-th element in the sample s.
The function returns a value for the mean point estimator.
Emilio Lopez Escobar.
Horvitz, D. G. and Thompson, D. J. (1952) A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47, 663–685.
Narain, R. D. (1951) On sampling without replacement with varying probabilities. Journal of the Indian Society of Agricultural Statistics, 3, 169–175.
Est.Mean.Hajek
VE.HT.Mean.NHT
VE.SYG.Mean.NHT
VE.Hajek.Mean.NHT
data(oaxaca) #Loads the Oaxaca municipalities dataset pik.U <- Pk.PropNorm.U(373, oaxaca$HOMES00) #Reconstructs the 1st order incl. probs. s <- oaxaca$sHOMES00 #Defines the sample to be used N <- dim(oaxaca)[1] #Defines the population size y1 <- oaxaca$POP10 #Defines the variable of interest y1 y2 <- oaxaca$HOMES10 #Defines the variable of interest y2 Est.Mean.NHT(y1[s==1], pik.U[s==1], N) #The NHT estimator for y1 Est.Mean.NHT(y2[s==1], pik.U[s==1], N) #The NHT estimator for y2
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.