Walsh averages

Calculates the set of Walsh (all pairwise) averages. Missing values are silently excluded.

Usage

walsh(x, sort = FALSE)

Arguments

x

(numeric)
The numeric vector used to calculate the Walsh averages. Missing values are silently excluded.

sort

(Scalar logical: FALSE)
Whether or not the vector of walsh averages should be sorted.

Value

numeric

Details

The set of Walsh (all pairwise) averages is defined as

$$ w_{ij} = \frac{x_i + x_j}{2}, \quad \text{for } 1 \leq i \leq j \leq n. $$

The Hodges-Lehman pseudomedian is computed as the median of the Walsh averages.

Examples

#----------------------------------------------------------------------------
# walsh() example
#----------------------------------------------------------------------------
library(bkstat)

walsh(1:3)
#> [1] 1.0 1.5 2.0 2.0 2.5 3.0
walsh(c(1:3, NA))
#> [1] 1.0 1.5 2.0 2.0 2.5 3.0

median(walsh(1:3))
#> [1] 2