finite.breakdown: Finite-sample breakdown point of various estimators

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/rQCC-Rprogram.R

Description

Calculates the finite-sample breakdown point of the mean, median, Hodges-Lehmann estimators (HL1, HL2, HL3), standard deviation, range, MAD (median absolute deviation) and Shamos estimators. Note that for the case of the mean, standard deviation and range, the finite-sample breakdown points are always zero.

Usage

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finite.breakdown(n, 
       method=c("mean","median","HL1","HL2","HL3","sd","range","mad","shamos") ) 

Arguments

n

sample size (n ≥ 1).

method

a character string specifying the estimator, must be one of "mean" (default), "median", "HL1", "HL2", "HL3", "sd", "range", "mad", and "shamos".

Details

finite.breakdown gives the finite-sample breakdown point of the specified estimator.

The Hodges-Lehmann (HL1) is defined as

HL1 = median of (X i+Xj)/2 over i<j

where i, j=1,2,...,n.

The Hodges-Lehmann (HL2) is defined as

HL2 = median of (Xi+Xj)/2 over i ≤ j.

The Hodges-Lehmann (HL3) is defined as

HL3 = median of (Xi+Xj)/2 over all (i,j).

Value

It returns a numeric value.

Author(s)

Chanseok Park and Min Wang

References

Park, C., H. Kim, and M. Wang (2020). Investigation of finite-sample properties of robust location and scale estimators. Communications in Statistics - Simulation and Computation, To appear.
https://doi.org/10.1080/03610918.2019.1699114

Hodges, Jr., J. L. (1967). Efficiency in normal samples and tolerance of extreme values for some estimates of location. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, 163–186, Berkeley. University of California Press.

Hampel, F. R., Ronchetti, E., Rousseeuw, P. J., and Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions, Subsection 2.2a. John Wiley & Sons, New York.

See Also

HL{rQCC} for the Hodges-Lehmann estimate.

Examples

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# finite-sample breakdown point of the Hodges-Lehmann (HL1) with size n=10.
finite.breakdown(n=10, method="HL2")

rQCC documentation built on March 26, 2020, 7:53 p.m.