dir_out function

Dai & Genton (2019) Directional outlyingness for univariate or multivariate functional data.

Compute the directional outlyingness of a univariate or multivariate functional data based on Dai and Genton (2019) tools:::Rd_expr_doi("10.1016/j.csda.2018.03.017")

and Dai and Genton (2018) tools:::Rd_expr_doi("10.1080/10618600.2018.1473781") .

dir_out(
  dts,
  data_depth = "random_projections",
  n_projections = 200L,
  seed = NULL,
  return_distance = TRUE,
  return_dir_matrix = FALSE
)

Arguments

• dts: A matrix (or data frame) for univariate functional data (of size n observations by p domain points) or a 3-dimensional array for multivariate functional data (of size n

  observations by p domain points by d dimension).

• data_depth: The method for computing the depth. The random projection depth is always used as suggested in Dai and Genton (2018) tools:::Rd_expr_doi("10.1080/10618600.2018.1473781") . Support for more depth methods will be added.

• n_projections: The number of directions for computing random projection depth. By default, 200 random directions are generated from a scaled uniform distribution between -1 and 1.

• seed: An integer indicating the seed to set when generating the random directions. Defaults to NULL in which case a seed is not set.

• return_distance: A logical value. If TRUE, returns: a matrix whose columns are the mean and variation of directional outlyingness, the mahalanobis distance of the observations of this matrix, and the robust estimate of the mean and covariance of this matrix (computed using the minimum covariance determinant method).

• return_dir_matrix: A logical value. If TRUE, returns the directional outlyingness matrix (or array for multivariate functional data). Computed from the chosen depth_depth.

Returns

Returns a list containing: - mean_outlyingness: an n x d matrix of the mean of directional outlyingness. - var_outlyingness: a vector of length n containing the variation of directional outlyingness.

• ms_matrix: ifreturn_distance = T, an n x (d+1) matrix whose columns are the mean and variation of directional outlyingness.

• distance: if return_distance = T, a vector of distance computed from the ms_matrix using a robust estimate of the mean and covariance matrix.

• mcd_obj: if return_distance = T, a list containing the robust (minimum covariance determinant) estimate of the mean and covariance of the ms_matrix.

• dirout_matrix: if return_dir_matrix = T, an n x p (or n x p x d) matrix (or array) containing the directional outlyingness values for the univariate (or multivariate) functional dts.

Details

The directional outlyingness, as defined in Dai and Genton (2019) tools:::Rd_expr_doi("10.1016/j.csda.2018.03.017") is

where $d$ is a depth notion, and $v$ is the unit vector pointing from the median of $F_Y$ to $Y$. For univariate and multivariate functional data, the projection depth is always used as suggested by Dai and Genton (2019) tools:::Rd_expr_doi("10.1016/j.csda.2018.03.017") .

Examples

# univariate magnitude model in Dai and Genton (2018).
dt4 <- simulation_model4()
dirout_object <- dir_out(dts = dt4$data, return_distance = TRUE)

References

Dai, W., and Genton, M. G. (2018). Multivariate functional data visualization and outlier detection. Journal of Computational and Graphical Statistics, 27(4), 923-934.

Dai, W., and Genton, M. G. (2019). Directional outlyingness for multivariate functional data. Computational Statistics & Data Analysis, 131, 50-65.

Zuo, Y. (2003). Projection-based depth functions and associated medians. The Annals of Statistics, 31(5), 1460-1490.

See Also

msplot for outlier detection using msplot and projection_depth

for multivariate projection depth.

Author(s)

Oluwasegun Taiwo Ojo.