Joint depth-median for vector-valued functional data

The median of a tf_mv vector is the single observed curve with maximal joint depth (see tf_depth()): one which.max index selects the same observation across every component, so the result is never a "chimera" stitched together from different curves. Note the deliberate divergence from median.tf() on ties: the univariate median averages tied maximal-depth curves, but averaging components would break the observed-curve guarantee, so median.tf_mv returns the first tied curve (with a message). On tied data, median(f)$x and median(f$x) can therefore differ.

Usage

# S3 method for class 'tf_mv'
median(x, na.rm = FALSE, depth = "MBD", ...)

Arguments

x

a tf_mv vector.

na.rm

if FALSE (default), any NA observation makes the result NA; if TRUE, NA observations are dropped first.

depth

the joint depth method, see tf_depth().

...

passed to tf_depth().

Value

a length-1 tf_mv: the observed curve with maximal joint depth.

See also

Other tidyfun summary functions: fivenum(), functionwise, tfsummaries

Examples

set.seed(1)
f <- tfd_mv(list(x = tf_rgp(5), y = tf_rgp(5)))
# the joint median is the observed curve with maximal joint depth:
median(f)
#> tfd_mv<d=2>[1] (x, y): [0, 1] -> [-0.4774177, 1.137399] x [-0.1362092, 1.230932]
#> components based on 51 evaluations each, interpolation by tf_approx_linear
#> [1]: ▆▇████▇▇▆▅▄▃▃▃▃▄▄▅▆▆▆▆▅▃▂▁ | ▃▃▃▃▃▃▃▃▃▃▂▂▁▁▁▁▁▁▂▃▄▆▇███
#> 
tf_depth(f)
#>     1     2     3     4     5 
#> 1.333 1.351 1.196 1.025 1.095