weighted_mean_winsorized function

Weighted Winsorized Mean and Total (bare-bone functions)

Weighted winsorized mean and total (bare-bone functions with limited functionality; see svymean_winsorized and svytotal_winsorized for more capable methods)

weighted_mean_winsorized(x, w, LB = 0.05, UB = 1 - LB, info = FALSE,
                         na.rm = FALSE)
weighted_mean_k_winsorized(x, w, k, info = FALSE, na.rm = FALSE)
weighted_total_winsorized(x, w, LB = 0.05, UB = 1 - LB, info = FALSE,
                          na.rm = FALSE)
weighted_total_k_winsorized(x, w, k, info = FALSE, na.rm = FALSE)

Arguments

• x: [numeric vector] data.
• w: [numeric vector] weights (same length as x).
• LB: [double] lower bound of winsorization such that $0 \leq$ LB $<$ UB $\leq 1$.
• UB: [double] upper bound of winsorization such that $0 \leq$ LB $<$ UB $\leq 1$.
• 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).
• k: [integer] number of observations to be winsorized at the top of the distribution.

Details

• Characteristic.: Population mean or total. Let $\mu$

   denote the estimated winsorized population mean; then, the estimated population total is given by $Nhat \mu$
   
   with $Nhat = sum(w[i])$, where summation is over all observations in the sample.
  

• Modes of winsorization.: The amount of winsorization can be specified in relative or absolute terms:

    * **Relative:** By specifying `LB` and `UB`, the methods winsorizes the `LB`$~\cdot 100\%$
      
      of the smallest observations and the (1 - `UB`)$~\cdot 100\%$ of the largest observations from the data.
    * **Absolute:** By specifying argument `k` in the functions with the "infix" `_k_` in their name, the largest $k$ observations are winsorized, $0\<k\<n$, where $n$ denotes the sample size. E.g., `k = 2`
      
      implies that the largest and the second largest observation are winsorized.
  

• Variance estimation.: See survey methods:

    * `svymean_winsorized`,
    * `svytotal_winsorized`,
    * `svymean_k_winsorized`,
    * `svytotal_k_winsorized`.
  

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]`
  

See Also

Overview (of all implemented functions)

svymean_winsorized, svymean_k_winsorized, svytotal_winsorized and svytotal_k_winsorized

Examples

head(workplace)

# Estimated winsorized population mean (5% symmetric winsorization)
weighted_mean_winsorized(workplace$employment, workplace$weight, LB = 0.05)

# Estimated one-sided k winsorized population total (2 observations are
# winsorized at the top of the distribution)
weighted_total_k_winsorized(workplace$employment, workplace$weight, k = 2)