robsurvey (version 0.7)

weighted_mean_dalen: 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)

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]

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.

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)