statsmodels.robust.covariance.CovDetMM#

class statsmodels.robust.covariance.CovDetMM(data, norm=None, breakdown_point=0.5, efficiency=0.95)[source]#

MM estimator using DetS as first stage estimator

Note: The tuning parameter for second stage M estimator is currently only available for a small number of variables and only three values of efficiency. For other cases, the user has to provide the norm instance with desired tuning parameter.

Changed in version 0.15.1: The breakdown_point argument is now used to compute the tuning parameter of the first stage S-estimator. Before, the tuning parameter for a breakdown point of 0.5 was always used.

Parameters:

dataarray_like: Multivariate data set with observation in rows and variables in columns.
normnorm instance, optional: If None, then TukeyBiweight norm is used. (Currently no other norms are supported for calling the initial S-estimator) If norm is an instance of TukeyBiweight, then it will be used in the second stage M-estimation. The efficiency argument is ignored and the tuning parameter of the user provided instance is not changed.
breakdown_pointfloat, optional: Breakdown point for first stage S-estimator. Must be in the interval (0, 0.5]. The tuning parameter of the norm of the first stage is chosen such that the expected rho under the multivariate normal model equals breakdown_point times the maximum of rho.
efficiencyfloat, optional: Asymptotic efficiency of second stage M estimator.

Raises:

ValueError: If breakdown_point is not in (0, 0.5], or if the tuning parameter of the first stage cannot be computed for the combination of breakdown_point and the number of variables.

Notes

Current limitation is that only TukeyBiweight is supported.

The tuning parameter for second stage M estimator uses a table of values for number of variables up to 15 and efficiency in [0.75, 0.8, 0.85, 0.9, 0.95, 0.975, 0.99]. The tuning parameter for other cases needs to be computed by numerical integration and rootfinding. Alternatively, the user can provide a norm instance with desired tuning parameter.

References

[1]

Hubert, Mia, Peter Rousseeuw, Dina Vanpaemel, and Tim Verdonck. 2015. “The DetS and DetMM Estimators for Multivariate Location and Scatter.” Computational Statistics & Data Analysis 81 (January): 64-75. https://doi.org/10.1016/j.csda.2014.07.013.

[2]

Hubert, Mia, Peter J. Rousseeuw, and Tim Verdonck. 2012. “A Deterministic Algorithm for Robust Location and Scatter.” Journal of Computational and Graphical Statistics 21 (3): 618-37. https://doi.org/10.1080/10618600.2012.672100.

[3]

Lopuhaä, Hendrik P. 1989. “On the Relation between S-Estimators and M-Estimators of Multivariate Location and Covariance.” The Annals of Statistics 17 (4): 1662-83.

[4]

Salibián-Barrera, Matías, Stefan Van Aelst, and Gert Willems. 2006. “Principal Components Analysis Based on Multivariate MM Estimators with Fast and Robust Bootstrap.” Journal of the American Statistical Association 101 (475): 1198-1211.

[5]

Tatsuoka, Kay S., and David E. Tyler. 2000. “On the Uniqueness of S-Functionals and M-Functionals under Nonelliptical Distributions.” The Annals of Statistics 28 (4): 1219-43.

Methods

fit([maxiter])

Estimate model parameters