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Unbiased Median Absolute Deviation

Source: R/umad.R
umad.Rd

This function calculates the Median Absolute Deviation (MAD) scale estimator for a numeric vector, using the Park-Kim-Wang approach. The method adds a small sample correction factor to make MAD unbiased at the normal distribution.

Usage

umad(x, method = "hayes", drop.na = TRUE)

Arguments

x

A numeric vector.

method

A character string specifying the method to use for calculating the correction factor when the number of sample is more than 100. The available options are "hayes" (default) and "williams".

drop.na

A logical value indicating whether to remove missing values (NA) from the calculations. If TRUE (the default), missing values will be removed. If FALSE, missing values will be included.

Value

The MAD scale estimate for the input vector x.

Details

The correction factor, \(C\), is calculated differently based on the sample size \(n\):

  • For \(n > 100\), \(C\) is calculated using an analytical approximation proposed by either Hayes (2014) or Williams (2011).

  • For \(n \leq 100\), \(C\) is obtained from a pre-computed table of values proposed by Park et al. (2020).

References

  • Park, C., Kim, H., Wang, M., (2020). Investigation of finite-sample properties of robust location and scale estimators. Communications in Statistics - Simulation and Computation, 51(5):2619–2645.

  • Hayes, K., (2014). Finite-Sample Bias-Correction Factors for the Median Absolute Deviation.Communications in Statistics - Simulation and Computation, 43(10):2205–2212.

  • Williams, D.C., (2011). Finite sample correction factors for several simple robust estimators of normal standard deviation. Journal of Statistical Computation and Simulation, 81(11):1697–1702.

Author

Christian L. Goueguel