Multiplicity (point) estimator of a total from an area sample of points

Each point that hits an establishment contributes y / expected_hits of that establishment; the sum over hits is unbiased for the population total whatever the number of times an establishment is hit (the more points fall on an establishment, the larger its contribution, matching its larger chance of selection). The variance is estimated at the cell level (ultimate-cluster approximation): the cell contributions are treated as cell totals and the variance estimator of the cell design is applied (local-mean for "lpm", replicates for replicated systematic samples, simple random sampling otherwise). With replicated systematic samples the expected hits refer to the union of the replicates, so the replicate variance is an approximation.

Usage

point_estimator(hits, sample)

Arguments

hits

Data frame with one row per point that hit an establishment: columns unit (cell), establishment, y (value of the whole establishment) and expected_hits (from expected_hits()).

sample

The fieldopt_sample of cells.

Value

A one-row tibble as in design_variance(), with n_hits and n_establishments.