Jackknife variance for survey estimates

For the delete-one jackknife of an unweighted mean the estimator reduces algebraically to s^2 / n, the textbook variance of the sample mean, which is the check the tests apply. Replicate weights may be supplied instead, in which case each replicate is whatever the supplied weights make it.

Usage

Jackvar(y, weights = NULL, replicates = NULL)

Arguments

y

Observations.

weights

Optional full-sample weights; equal by default.

replicates

Optional R x n matrix of replicate weight sets; the delete-one jackknife by default.

Value

List with estimate, variance, theta, theta_replicates, se, n, method.

Details

Formula: v_J = ((R - 1)/R) sum_r (theta_r - theta)^2.

References

Wolter (2007), Introduction to Variance Estimation, 2nd ed., Springer, ch. 4, eq. (4.2.5).

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Jackvar(V)
#> $estimate
#> [1] 0.75
#> 
#> $variance
#> [1] 0.75
#> 
#> $theta
#> [1] 4.5
#> 
#> $theta_replicates
#> [1] 5.000000 4.857143 4.714286 4.571429 4.428571 4.285714 4.142857 4.000000
#> 
#> $se
#> [1] 0.8660254
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "v_J = ((R-1)/R) sum_r (theta_r - theta)^2, Wolter (2007) eq. (4.2.5)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"