fdaoutlier (version 0.2.1)

extremal_depth: Compute extremal depth for functional data

Description

Compute extremal depth for functional data

Usage

extremal_depth(dts)

Value

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

Arguments

dts

A numeric matrix or dataframe of size \(n\) observations/curves by \(p\) domain/evaluation points.

Author

Oluwasegun Ojo

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").

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.

Examples

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