HL: Hodges-Lehmann estimator

In rQCC: Robust Quality Control Chart

Hodges-Lehmann estimator

Description

Calculates the Hodges-Lehmann estimator.

Usage

HL(x, estimator = c("HL1", "HL2", "HL3"), na.rm = FALSE)

Arguments

x	a numeric vector of observations.
estimator	a character string specifying the estimator, must be one of "HL1" (default), "HL2" and "HL3".
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.

Details

HL computes the Hodges-Lehmann estimators (one of "HL1", "HL2", "HL3").

The Hodges-Lehmann (HL1) is defined as

HL1 = median of (Xi+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 (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

Hodges, J. L. and E. L. Lehmann (1963). Estimates of location based on rank tests. Annals of Mathematical Statistics, 34, 598–611.

See Also

mean{base} for calculating sample mean and median{stats} for calculating sample median.

finite.breakdown{rQCC} for calculating the finite-sample breakdown point.

Examples

x = c(0:10, 50)
HL(x, estimator="HL2")

rQCC documentation built on Dec. 28, 2022, 1:49 a.m.