Hodges-Lehmann Estimator of Location

Function to compute the Hodges-Lehmann estimator of location in the one and two sample case following a clever fast algorithm by John Monahan (1984).

HodgesLehmann(x, y = NULL, conf.level = NA, na.rm = FALSE)

Arguments

x: a numeric vector.
y: an optional numeric vector of data values: as with x non-finite values will be omitted.
conf.level: confidence level of the interval.
na.rm: logical. Should missing values be removed? Defaults to FALSE.

Details

The Hodges-Lehmann estimator is the median of the combined data points and Walsh averages. It is the same as the Pseudo Median returned as a by-product of the function wilcox.test (which however does not calculate correctly as soon as ties are present).
Note that in the two-sample case the estimator for the difference in location parameters does not estimate the difference in medians (a common misconception) but rather the median of the difference between a sample from x and a sample from y.

(The calculation of the confidence intervals is not yet implemented.)

Value

the Hodges-Lehmann estimator of location as a single numeric value if no confidence intervals are requested,
and otherwise a numeric vector with 3 elements for the estimate, the lower and the upper confidence interval

References

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

Monahan, J. (1984), Algorithm 616: Fast Computation of the Hodges-Lehmann Location Estimator, ACM Transactions on Mathematical Software, Vol. 10, No. 3, pp. 265-270

Author

Cyril Flurin Moser (Cyril did the lion's share and coded Monahan's algorithm in C++), Andri Signorell <andri@signorell.net>

Examples

set.seed(1)
x <- rt(100, df = 3)
y <- rt(100, df = 5)

HodgesLehmann(x)
#> [1] -0.04253799
HodgesLehmann(x, y)
#> [1] -0.1090921

# same as
wilcox.test(x, conf.int = TRUE)$estimate
#> (pseudo)median 
#>    -0.04251537