rQCC (version 2.22.12)

finite.sample.breakdown: Finite-sample breakdown point

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

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

Value

It returns a numeric value.

Arguments

n

a numeric vector of sample sizes.

estimator

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

Author

Chanseok Park and Min Wang

Details

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

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 (2022). Investigation of finite-sample properties of robust location and scale estimators. Communications in Statistics - Simulation and Computation, 51, 2619-2645.
tools:::Rd_expr_doi("10.1080/03610918.2019.1699114")

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

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 estimator.

Examples

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

# finite-sample breakdown points of the median with sizes n=4,5,6 
finite.breakdown(n=4:6, estimator="median")