weighted_mean_dalen function

Dalen Estimators of the Mean and Total

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

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 $sum(w[i]x[i])$ 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 $min(c, w[i]x[i]$; hence, it censors the products $w[i]x[i]$ 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 $z[i] = w[i]x[i]$

   if $w[i]x[i] <= c$ and $z[i] = c + (y[i] - c/w[i])$
   
   otherwise.
  

Returns

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)