extremal_depth function

Compute extremal depth for functional data

extremal_depth(dts)

Arguments

• dts: A numeric matrix or dataframe of size $n$ observations/curves by $p$ domain/evaluation points.

Returns

A vector containing the extremal depths of the rows of dts.

Details

This function computes the extremal depth of a univariate functional data. The extremal depth of a function $g$ with respect to a set of function $S$ denoted by $ED(g, S)$ is the proportion of functions in $S$ that is more extreme than $g$. The functions are ordered using depths cumulative distribution functions (d-CDFs). Extremal depth like the name implies is based on extreme outlyingness and it penalizes functions that are outliers even for a small part of the domain. Proposed/mentioned in Narisetty and Nair (2016) tools:::Rd_expr_doi("10.1080/01621459.2015.1110033") .

Examples

dt3 <- simulation_model3()
ex_depths <- extremal_depth(dts = dt3$data)
# order functions from deepest to most outlying
order(ex_depths, decreasing = TRUE)

References

Narisetty, N. N., & Nair, V. N. (2016). Extremal depth for functional data and applications. Journal of the American Statistical Association, 111(516), 1705-1714.

@seealso total_variation_depth for functional data.

Author(s)

Oluwasegun Ojo