weighted_mean_tukey: Weighted Tukey Mean and Total (bare-bone functions)

In robsurvey: Robust Survey Statistics Estimation

Weighted Tukey Mean and Total (bare-bone functions)

Description

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

Usage

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 vector x).
k	[double] robustness tuning constant (0 < k <= Inf).
type	[character] type of method: "rwm" or "rht"; see below (default: "rwm").
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 μ denote the estimated population mean; then, the estimated total is given by Nhat μ with Nhat = sum(w[i]), where summation is over all observations in the sample.

Type.

Two methods/types are available for estimating the location:

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 survey methods:

• svymean_tukey,

• svytotal_tukey.

Psi-function.

Tukey biweight (or bisquare) psi-function with tuning parameter k

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]

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.

References

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

See Also

Overview (of all implemented functions)

weighted_mean_huber and weighted_total_huber

Examples

data(workplace)

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

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

robsurvey documentation built on Jan. 6, 2023, 5:09 p.m.