Jackknife estimate, standard error and confidence interval

Applies a statistic to the point weights and to every delete-a-PSU replicate, and summarises it with the stratified jackknife (JKn) variance $$\sum_h \frac{n_h - 1}{n_h} \sum_{i \in h} (\theta_{(hi)} - \bar\theta_h)^2,$$ where $\theta_{(hi)}$ is the estimate with PSU $i$ of stratum $h$ deleted and $\bar\theta_h$ the mean of those over the stratum. No finite population correction is applied.

Usage

jackknife_estimate(jack, statistic, level = 0.95)

jack_total(jack, variable)

jack_mean(jack, variable)

Arguments

jack: a weightflow_jack object.
statistic: a function function(w, data) returning a numeric scalar (or vector) given a weight vector and the data.
level: confidence level for the (normal) interval.
variable: name of the variable to estimate (for jack_total/jack_mean).

Value

A data frame with estimate, se, ci_lower, ci_upper.

Note

jack_total() / jack_mean() center the replicate deviations on the per-stratum mean of the deleted-PSU estimates (the standard JKn). The survey design built by as_svrepdesign() instead uses mse = TRUE, which centers on the point estimate. Both are legitimate, so the standard errors from jack_total() and from svytotal() on the same object can differ slightly.

Examples

spec <- weighting_spec(sample_one, base_weights = pw) |>
  step_calibrate(method = "raking",
                 margins = list(region = c(table(population$region))))
jk <- jackknife_weights(spec, strata = "region", psu = "psu", progress = FALSE)
jackknife_estimate(jk, function(w, d) sum(w * d$employed, na.rm = TRUE))
#>   estimate       se ci_lower ci_upper
#> 1 1031.456 85.28049 864.3092 1198.603