weighted_mean_dalen {robsurvey}

Dalen Estimators of the Mean and Total

Description

Dalén's estimators of the population mean and the population total (bare-bone functions with limited functionality).

Usage

weighted_mean_dalen(x, w, censoring, type = "Z2", info = FALSE,
                    na.rm = FALSE, verbose = TRUE)
weighted_total_dalen(x, w, censoring, type = "Z2", info = FALSE,
                     na.rm = FALSE, verbose = TRUE)

Arguments

x

[numeric vector] data.

w

[numeric vector] weights (same length as x).

censoring

[double] cutoff threshold above which the observations are censored.

type

[character] type of estimator; either "Z2" or "Z3" (default: "Z2").

info

[logical] indicating whether additional information should be returned (default: FALSE).

na.rm

[logical] indicating whether NA values should be removed before the computation proceeds (default: FALSE).

verbose

[logical] indicating whether additional information should be printed to the console (default: FALSE).

Details

Let \sum_{i \in s} w_ix_i denote the expansion estimator of the x-total (summation is over all elements i in sample s). The estimators Z2 and Z3 of Dalén (1987) are defined as follows.

Estimator Z2

The estimator Z2 of the population total sums over \min(c, w_ix_i); hence, it censors the products w_ix_i to the censoring constant c (censoring). The estimator of the population x-mean is is defined as the total divided by the population size.

Estimator Z3

The estimator Z3 of the population total is defined as the sum over the elements z_i, which is equal to z_i = w_ix_i if w_iy_i \leq c and z_i = c + (y_i - c/w_i) otherwise.

Value

The return value depends on info:

info = FALSE:

estimate of mean or total [double]

info = TRUE:

a [list] with items:

• characteristic [character],

• estimator [character],

• estimate [double],

• variance (default: NA),

• robust [list],

• residuals [numeric vector],

• model [list],

• design (default: NA),

• [call]

References

Dalén, J. (1987). Practical Estimators of a Population Total Which Reduce the Impact of Large Observations. R & D Report U/STM 1987:32, Statistics Sweden, Stockholm.

See Also

Overview (of all implemented functions)

Examples

head(workplace)

# Dalen's estimator of the total (with censoring threshold: 100000)
weighted_total_dalen(workplace$employment, workplace$weight, 100000)