n.times.eBias {rQCC}

Empirical biases (times n)

Description

n times the empirical biases of the median absolute deviation (MAD) and Shamos estimators.

Usage

n.times.eBias.of.mad

n.times.eBias.of.shamos

Details

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.

Value

They return a vector of 100 values.

Author(s)

Chanseok Park and Min Wang

References

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.
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.