weighted-m-estimator function

Weighted Huber and Tukey Mean and Total (bare-bone functions)

Weighted Huber and Tukey M-estimator of the mean and total (bare-bone function with limited functionality; see svymean_huber, svymean_tukey, svytotal_huber, and svytotal_tukey for more capable methods)

weighted_mean_huber(x, w, k, type = "rwm", asym = FALSE, info = FALSE,
                    na.rm = FALSE, verbose = TRUE, ...)
weighted_total_huber(x, w, k, type = "rwm", asym = FALSE, info = FALSE,
                     na.rm = FALSE, verbose = TRUE, ...)
weighted_mean_tukey(x, w, k, type = "rwm", info = FALSE, na.rm = FALSE,
                    verbose = TRUE, ...)
weighted_total_tukey(x, w, k, type = "rwm", info = FALSE, na.rm = FALSE,
                     verbose = TRUE, ...)

Arguments

• x: [numeric vector] data.
• w: [numeric vector] weights (same length as x).
• k: [double] robustness tuning constant ($0 < k <= Inf$).
• type: [character] type of method: "rwm" or "rht"; see below (default: "rwm").
• asym: [logical] toggle for asymmetric Huber psi-function (default: FALSE).
• 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 is printed to the console (default: TRUE).
• ...: additional arguments passed to the method (e.g., maxit: maxit number of iterations, etc.).

Details

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

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

• Type.: Two methods/types are available for estimating the location $\mu$:

   - **`type = "rwm" (default)`:**: robust weighted **M**-estimator of the population mean and total, respectively. This estimator is recommended for sampling designs whose inclusion probabilities are **not**
          
          proportional to some measure of size. [Legacy note: In an earlier version, the method `type = "rwm"` was called `"rhj"`; the type `"rhj"` is now silently converted to `"rwm"`]
   - **`type = "rht"`:**: robust Horvitz-Thompson **M**-estimator of the population mean and total, respectively. This estimator is recommended for proportional-to-size sampling designs.
  

• Variance estimation.: See the related but more capable functions:

    * `svymean_huber` and `svymean_tukey`,
    * `svytotal_huber` and `svytotal_tukey`.
  

• Psi-function.: By default, the Huber or Tukey

   psi-function are used in the specification of the M-estimators. For the Huber estimator, an asymmetric version of the Huber psi-function can be used by setting the argument `asym = TRUE` in the function call.
  

Failure of convergence

By default, the method assumes a maximum number of maxit = 100

iterations and a numerical tolerance criterion to stop the iterations of tol = 1e-05. If the algorithm fails to converge, you may consider changing the default values; see svyreg_control.

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

Hulliger, B. (1995). Outlier Robust Horvitz-Thompson Estimators. Survey Methodology 21 , 79--87.

See Also

Overview (of all implemented functions)

Examples

head(workplace)

# Robust Horvitz-Thompson M-estimator of the population total
weighted_total_huber(workplace$employment, workplace$weight, k = 9,
    type = "rht")

# Robust weighted M-estimator of the population mean
weighted_mean_huber(workplace$employment, workplace$weight, k = 12,
    type = "rwm")