rQCC (version 0.19.8.2)

Hodges-Lehmann: Hodges-Lehmann estimate

Description

Calculates the Hodges-Lehmann estimate.

Usage

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

Arguments

x

a numeric vector of observations.

method

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.

Value

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

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

See Also

base::mean for calculating sample mean and stats::median for calculating sample median.

rQCC::finite.breakdown for calculating the finite-sample breakdown point.

Examples

# NOT RUN {
x = c(0:10, 50)
HL(x, method="HL2")
# }