statsmodels.robust.covariance.CovDetMM

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

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.

Parameters:

dataarray_like

Multivariate data set with observation in rows and variables in columns.

normnorm instance

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 in (0, 0.5]

Breakdown point for first stage S-estimator.

efficiencyfloat

Asymptotic efficiency of second stage M estimator.

Methods

fit([maxiter])

Estimate model parameters

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