Ratio estimate of a mean or total, using an auxiliary variable

The estimator is biased; the bias is O(1/n) and is not corrected here, matching Cochran's Chapter 6 treatment.

Usage

Ratioest(y, x, X = NULL, N = Inf, level = 0.95)

Arguments

y

Sample values of the variable of interest.

x

Sample values of the auxiliary variable; xbar non-zero.

X

Known population TOTAL of x (optional).

N

Population size, for the finite population correction.

level

Confidence level.

Value

List with ratio, se_ratio, ci_lower, ci_upper, total, se_total, residual_var, fpc, n.

Details

Formula: Rhat = ybar/xbar; Yhat_R = Rhat X; v(Rhat) = (1 - f)/(n xbar^2) * sum (y_i - Rhat x_i)^2/(n - 1)

References

Cochran (1977), Sampling Techniques, 3rd edition, Chapter 6. Chapter 6 was NOT in the scanned excerpt available to this batch, so the standard published form is used; the finite-population factor matches the samplingbook 1.2.4 convention (N - n)/N used throughout the sibling Cochran modules.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Ratioest(V, V)
#> $ratio
#> [1] 1
#> 
#> $se_ratio
#> [1] 0
#> 
#> $ci_lower
#> [1] 1
#> 
#> $ci_upper
#> [1] 1
#> 
#> $total
#> [1] NaN
#> 
#> $se_total
#> [1] NaN
#> 
#> $residual_var
#> [1] 0
#> 
#> $fpc
#> [1] 1
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Ratio estimator, Cochran Chapter 6"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"