rQCC (version 0.19.8.2)

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

Description

Calculates finite-sample breakdown point of median, Hodges-Lehmann estimators (HL1, HL2, HL3), MAD (median absolute deviation) and Shamos.

Usage

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

Arguments

n

sample size (\(n \ge 1\)).

method

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

Value

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

Details

The Hodges-Lehmann (HL1) is defined as $$\mathrm{HL1} = \mathop{\mathrm{median}}_{i<j} \Big( \frac{X_i+X_j}{2} \Big).$$ where \(i,j=1,2,\ldots,n\).

The Hodges-Lehmann (HL2) is defined as $$\mathrm{HL2} = \mathop{\mathrm{median}}_{i \le j}\Big(\frac{X_i+X_j}{2} \Big).$$

The Hodges-Lehmann (HL3) is defined as $$\mathrm{HL3} = \mathop{\mathrm{median}}_{\forall(i,j)} \Big( \frac{X_i+X_j}{2} \Big).$$

References

Park, C., H. Kim, and M. Wang (2019). Finite-sample properties of robust location and scale estimators. arXiv:1908.00462.

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

rQCC::HL for the Hodges-Lehmann estimate.

Examples

# NOT RUN {
# finite-sample breakdown point of the Hodges-Lehmann (HL1) with size n=10.
finite.breakdown(n=10, method="HL2")
# }