functional_boxplot: Functional Boxplot for a sample of functions.

In fdaoutlier: Outlier Detection Tools for Functional Data Analysis

Functional Boxplot for a sample of functions.

Description

This function finds outliers in a sample of curves using the functional boxplot by Sun and Genton (2011) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/jcgs.2011.09224")}. Unlike the name suggests, the function does not actually produce a plot but is only used as support in finding outliers in other functions. Different depth and outlyingness methods are supported for ordering functions. Alternatively, the depth values of the functions can be supplied directly.

Usage

functional_boxplot(
  dts,
  depth_method = c("mbd", "tvd", "extremal", "dirout", "linfinity", "bd", "erld", "dq"),
  depth_values = NULL,
  emp_factor = 1.5,
  central_region = 0.5,
  erld_type = NULL,
  dq_quantiles = NULL
)

Arguments

dts	A matrix or data frame of size n observations/curves by p domain/evaluation points for univariate functional data.
depth_method	A character value specifying the method to use for computing the depth values (if depth_values is not supplied) used in ordering the functions. The following methods are are supported: "mbd": The modified band depth with bands defined by 2 functions. Uses the algorithm of Sun et al. (2012)\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sta4.8")}. "tvd" The total variation depth of Huang and Sun (2019) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00401706.2019.1574241")}. "extremal" The extremal depth of Narisetty and Nair (2016) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.2015.1110033")}. "dirout" Uses the robust distance of the mean and variation of directional outlyingness (dir_out) defined in Dai and Genton (2019) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.csda.2018.03.017")}. Since this method is a measure of outlyingness of a function the negative of the computed robust distance is used in ordering the functions. "linfinity" The L-infinity depth defined in Long and Huang (2015) <arXiv:1506.01332 is used in ordering functions. "bd" Uses the band depth with bands defined by 2 functions according to the algorithm of Sun et al. (2012) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sta4.8")}. erld Uses the extreme rank length depth used in Dai et al. (2020) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.csda.2020.106960")}. "dq" Uses the directional quantile (DQ) used in Dai et al. (2020) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.csda.2020.106960")}. Since DQ is a measure of outlyingness, the negative of the DQ values is used in ordering the functions. The default method is "mbd". Alternatively, the depth_values of the functions can be supplied in which case the depths are not computed and depth_method is ignored.
depth_values	A numeric vector containing the depth values of the functions in dts to use for ordering functions. length(depth_values) must be equal to number of rows of dts. If depth_values is specified, the depth is not computed and any method specified in depth_method is ignored.
emp_factor	A numeric value specifying the empirical factor for the boxplot. Defaults to 1.5.
central_region	A numeric value between 0 and 1 indicating the probability of central region. Defaults to 0.5.
erld_type	If depth_method = "erld", the type of ordering to use in computing the extreme rank length depth. Can be one of "two_sided", "one_sided_left" or "one_sided_right". A "two_sided" ordering is used by default if erld_type is not specified. See extreme_rank_length for more details.
dq_quantiles	If depth_method = "dq", a numeric vector of length 2 specifying the probabilities of upper and lower quantiles. Defaults to c(0.025, 0.975) for the upper and lower 2.5% quantiles. See directional_quantile for details.

Value

A list containing:

outliers	The indices of the functions/curves flagged as outliers.
depth_values	The depths of the functions/curves in dts.
median_curve	The index of the median curve, which is the curve with the largest depth value (or smallest outlyingness value).

References

Sun, Y., & Genton, M. G. (2011). Functional boxplots. Journal of Computational and Graphical Statistics, 20(2), 316-334.

See Also

seq_transform for functional outlier detection using sequential transformation.

Examples

dt1 <- simulation_model1()
fbplot_obj <- functional_boxplot(dt1$data, depth_method = "mbd")
fbplot_obj$outliers

fdaoutlier documentation built on Oct. 1, 2023, 1:06 a.m.