BLE_Ratio {BayesSampling}

Ratio BLE

Description

Creates the Bayes Linear Estimator for the Ratio "estimator"

Usage

BLE_Ratio(ys, xs, x_nots, m = NULL, v = NULL, sigma = NULL, n = NULL)

Arguments

ys

vector of sample observations or sample mean (sigma and n parameters will be required in this case).

xs

vector with values for the auxiliary variable of the elements in the sample or sample mean.

x_nots

vector with values for the auxiliary variable of the elements not in the sample.

m

prior mean for the ratio between Y and X. If NULL, mean(ys)/mean(xs) will be used (non-informative prior).

v

prior variance of the ratio between Y and X (bigger than sigma^2). If NULL, it will tend to infinity (non-informative prior).

sigma

prior estimate of variability (standard deviation) of the ratio within the population. If NULL, sample variance of the ratio will be used.

n

sample size. Necessary only if ys and xs represent sample means (will not be used otherwise).

Value

A list containing the following components:

• est.beta - BLE of Beta

• Vest.beta - Variance associated with the above

• est.mean - BLE for each individual not in the sample

• Vest.mean - Covariance matrix associated with the above

• est.tot - BLE for the total

• Vest.tot - Variance associated with the above

Source

https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X201400111886

References

Gonçalves, K.C.M, Moura, F.A.S and Migon, H.S.(2014). Bayes Linear Estimation for Finite Population with emphasis on categorical data. Survey Methodology, 40, 15-28.

Examples

ys <- c(10,8,6)
xs <- c(5,4,3.1)
x_nots <- c(1,20,13,15,-5)
m <- 2.5
v <- 10
sigma <- 2

Estimator <- BLE_Ratio(ys, xs, x_nots, m, v, sigma)
Estimator


# Same example but informing sample means and sample size instead of sample observations
ys <- mean(c(10,8,6))
xs <- mean(c(5,4,3.1))
n <- 3
x_nots <- c(1,20,13,15,-5)
m <- 2.5
v <- 10
sigma <- 2

Estimator <- BLE_Ratio(ys, xs, x_nots, m, v, sigma, n)
Estimator