Rousseeuw-Croux Scale Estimators

This function calculates either the Rousseeuw-Croux Sn or Qn scale estimator.

Usage

rousseeuwCroux(x, estimator = c("Sn", "Qn"), drop.na = FALSE)

Arguments

x

A numeric vector of data values.

estimator

A character string indicating whether to calculate the "Sn" or "Qn" estimator.

drop.na

A logical value indicating whether to remove missing values (NA) from the input vector.

Value

A numeric value representing the calculated Sn or Qn scale estimator.

Details

The Sn and Qn estimators, proposed by Rousseeuw and Croux (1993), are robust measures of scale (or dispersion) that are designed to have a high breakdown point, which is a desirable property for estimators in the presence of outliers or heavy-tailed distributions. Specifically, both estimators have a breakdown point of 50%. The Sn estimator is based on the median, while the Qn estimator is based on a weighted combination of order statistics. Both estimators are consistent estimators of the population scale parameter under normality. Although, the function uses the robustbase package for estimating Sn and Qn, the bias-correction factors used in the calculations have been, however, refined according to Akinshin, A., (2022).

References

• Rousseeuw, P.J. and Croux, C. (1993). Alternatives to the median absolute deviation. Journal of the American Statistical Association, 88(424):1273-1283.

• Akinshin, A., (2022). Finite-sample Rousseeuw-Croux scale estimators. arxiv:2209.12268v1.

Author

Christian L. Goueguel

Examples

# Example 1:
x <- c(seq(1,100))
tibble::tibble(
sd = stats::sd(x),
mad = stats::mad(x),
Sn = rousseeuwCroux(x, estimator = "Sn"),
Qn = rousseeuwCroux(x, estimator = "Qn")
)
#> # A tibble: 1 × 4
#>      sd   mad    Sn    Qn
#>   <dbl> <dbl> <dbl> <dbl>
#> 1  29.0  37.1  29.8  30.0

# Example 2:
x <- c(seq(1,99), 1e3) # An outlier at 1000
tibble::tibble(
sd = stats::sd(x),
mad = stats::mad(x),
Sn = rousseeuwCroux(x, estimator = "Sn"),
Qn = rousseeuwCroux(x, estimator = "Qn")
)
#> # A tibble: 1 × 4
#>      sd   mad    Sn    Qn
#>   <dbl> <dbl> <dbl> <dbl>
#> 1  99.2  37.1  31.0  30.0