\(n\) times the empirical biases of the median absolute deviation (MAD) and Shamos estimators.
n.times.eBias.of.madn.times.eBias.of.shamos
They return a vector of 100 values.
Chanseok Park and Min Wang
\(n\) times the empirical biases of the median absolute deviation (MAD)
and Shamos estimators
under the standard normal distribution, where \(n\) is the sample size
and \(n\) is from 1 to 100.
For the MAD estimator, mad{stats} is used.
For the Shamos estimator, the Fisher-consistent Shamos estimator, shamos{rQCC}, is used.
These estimators are not unbiased with a finite sample. The empirical biases are obtained using the extensive Monte Carlo simulation with 1E07 replicates.
Park, C., H. Kim, and M. Wang (2022).
Investigation of finite-sample properties of robust location and scale estimators.
Communications in Statistics - Simulation and Computation,
51, 2619-2645.
tools:::Rd_expr_doi("10.1080/03610918.2019.1699114")
Shamos, M. I. (1976). Geometry and statistics: Problems at the interface. In Traub, J. F., editor, Algorithms and Complexity: New Directions and Recent Results, pages 251--280. Academic Press, New York.
Lèvy-Leduc, C., Boistard, H., Moulines, E., Taqqu, M. S., and Reisen, V. A. (2011). Large sample behaviour of some well-known robust estimators under long-range dependence. Statistics, 45, 59--71.