L2-depth#
- L2(x, data, mah_estimate='moment', mah_parMcd=0.75)[source]#
- Description
Calculates the L2-depth of points w.r.t. a multivariate data set.
- Arguments
- x
Matrix of objects (numerical vector as one object) whose depth is to be calculated; each row contains a d-variate point. Should have the same dimension as data.
- data
Matrix of data where each row contains a d-variate point, w.r.t. which the depth is to be calculated.
- mah_estimate
Is a character string specifying which estimates to use when calculating sample covariance matrix; can be
'none','moment'or'MCD', determining whether traditional moment or Minimum Covariance Determinant (MCD) estimates for mean and covariance are used. By default'moment'is used. With'none'the non-affine invariant version of the L2-depth is calculated.- mah_parMcd
is the value of the argument alpha for the function covMcd; is used when
mah.estimate='MCD'.
- References
Zuo, Y. and Serfling, R. (2000). General notions of statistical depth function. The Annals of Statistics, 28, 461–482.
Mosler, K. and Mozharovskyi, P. (2022). Choosing among notions of multivariate depth statistics. Statistical Science, 37(3), 348-368.
- Examples
>>> import numpy as np >>> from depth.multivariate import * >>> mat1=[[1, 0, 0, 0, 0],[0, 2, 0, 0, 0],[0, 0, 3, 0, 0],[0, 0, 0, 2, 0],[0, 0, 0, 0, 1]] >>> mat2=[[1, 0, 0, 0, 0],[0, 1, 0, 0, 0],[0, 0, 1, 0, 0],[0, 0, 0, 1, 0],[0, 0, 0, 0, 1]] >>> x = np.random.multivariate_normal([1,1,1,1,1], mat2, 10) >>> data = np.random.multivariate_normal([0,0,0,0,0], mat1, 1000) >>> L2(x, data) [0.2867197 0.19718391 0.18896649 0.24623271 0.20979579 0.22055673 0.20396566 0.20779032 0.24901829 0.26734192]