n.times.eBias {rQCC}R Documentation

Empirical biases (times n)

Description

nn 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

nn times the empirical biases of the median absolute deviation (MAD) and Shamos estimators under the standard normal distribution, where nn is the sample size and nn 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.


[Package rQCC version 2.22.12 Index]