Geenens & Nieto-Reyes functional distance-based depth

Calculates a global distance-based depth vector using a distance matrix. Specifically we use Geenens & Nieto-Reyes's global distance-based depth defined as:

distance_depth_function(x, x_new = NULL, df_out = "auto")

# S3 method for matrix
distance_depth_function(x, x_new = NULL, df_out = F)

# S3 method for tidy_dist_mat
distance_depth_function(x, x_new = NULL, df_out = T)

Arguments

x	a n x n square positive symmetric matrix or a tidy_dist_mat
x_new	a n_new x n matrix or tidy_dist_mat where the rows correspond to new observations, the columns correspond to points in x (if x and x_new are matrices then they need to be corrected ordered). If this value is not NULL (default is NULL) then the depth vector will be calculated for these observations relative to observations defined with x and x_new's columns.
df_out	indicates if one should return a data.frame our a vector, by default returns data.frame if dist_mat is a tidy_dist_mat, and a vector if dist_mat is a matrix.

Value

depth vector length n with depth values associated with indices in dist_mat or a data.frame with a column called depth

Details

\(DD(x, \hat{P}) = 1/(n choose 2) \cdot \sum_{i!=j} I(d(X_i, X_j) > max(d(X_i,x), d(X_j,x)))\)

This function (renamed as depth_function) is shared with TCpredictionbands on github: TCpredictionbands.

Examples

dist_mat <- matrix(c(0,   1, 1.5,
                     1,   0, 2,
                     1.5, 2, 0   ),
                   nrow = 3,
                   byrow = TRUE)

dd_vec <- distance_depth_function(dist_mat) # c(1,0,0)

tidy_dm <- tidy_dist_mat(dist_mat)
dd_df <- distance_depth_function(tidy_dm) # depth = c(1,0,0)