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

View source: R/rQCC-Rprogram.R

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.

1 2 | ```
finite.breakdown(n,
method=c("mean","median","HL1","HL2","HL3","sd","range","mad","shamos") )
``` |

`n` |
sample size ( |

`method` |
a character string specifying the estimator, must be
one of |

`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).*

It returns a numeric value.

Chanseok Park and Min Wang

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.

`HL`

{rQCC} for the Hodges-Lehmann estimate.

1 2 | ```
# finite-sample breakdown point of the Hodges-Lehmann (HL1) with size n=10.
finite.breakdown(n=10, method="HL2")
``` |

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