weighted_mean_dalen: Dalen Estimators of the Mean and Total
In robsurvey: Robust Survey Statistics Estimation

weighted_mean_dalen

R Documentation

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.

Examples

head(workplace)

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

robsurvey documentation built on Sept. 11, 2024, 6:35 p.m.