vslSSEditRobustCovariance

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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vslSSEditRobustCovariance

Modifies pointers to arrays related to a robust covariance matrix.

Syntax

status = vslssseditrobustcovariance(task, rcov_storage, nparams, params, rmean, rcov)

status = vsldsseditrobustcovariance(task, rcov_storage, nparams, params, rmean, rcov)

Include Files

mkl_vsl.f90

Input Parameters

Name	Type	Description
task	Fortran: TYPE(VSL_SS_TASK)	Descriptor of the task
rcov_storage	Fortran: INTEGER	Pointer to the storage format of a robust covariance matrix
nparams	Fortran: INTEGER	Pointer to the number of method parameters
params	Fortran: REAL(KIND=4) DIMENSION() for vslssseditrobustcovariance REAL(KIND=8) DIMENSION() for vsldsseditrobustcovariance	Pointer to the array of method parameters
rmean	Fortran: REAL(KIND=4) DIMENSION() for vslssseditrobustcovariance REAL(KIND=8) DIMENSION() for vsldsseditrobustcovariance	Pointer to the array of robust means
rcov	Fortran: REAL(KIND=4) DIMENSION() for vslssseditrobustcovariance REAL(KIND=8) DIMENSION() for vsldsseditrobustcovariance	Pointer to a robust covariance matrix

Output Parameters

Name	Type	Description
status	Fortran: INTEGER	Current status of the task

Description

The vslSSEditRobustCovariance routine uses values passed as parameters of the routine to replace:

pointers to covariance matrix storage
pointers to the number of method parameters and to the array of the method parameters of size nparams
pointers to the arrays that hold robust means and covariance

See Table "Storage formats of a variance-covariance/correlation matrix" for possible values of the rcov_storage parameter. If you pass a value of NULL for a specific input parameter, the value of that parameter in the task descriptor is unchanged.

Intel® oneAPI Math Kernel Library provides a Translated Biweight S-estimator (TBS) for robust estimation of a variance-covariance matrix and mean [Rocke96]. Use one iteration of the Maronna algorithm with the reweighting step [Maronna02] to compute the initial point of the algorithm. Pack the parameters of the TBS algorithm into the params array and pass them into the editor. Table "Structure of the Array of TBS Parameters" describes the params structure.

Structure of the Array of TBS Parameters
Array Position	Algorithm Parameter	Description
0	ε	Breakdown point, the number of outliers the algorithm can hold. By default, the value is `(n-p)/(2n)`.
1	α	Asymptotic rejection probability, see details in [Rocke96]. By default, the value is 0.001.
2	δ	Stopping criterion: the algorithm is terminated if weights are changed less than δ. By default, the value is 0.001.
3	max_iter	Maximum number of iterations. The algorithm terminates after max_iter iterations. By default, the value is 10. If you set this parameter to zero, the function returns a robust estimate of the variance-covariance matrix computed using the Maronna method [Maronna02] only.

The robust estimator of variance-covariance implementation in Intel® oneAPI Math Kernel Library requires that the number of observationsn be greater than twice the number of variables: n > 2p.

See additional details of the algorithm usage model in the Intel® oneAPI Math Kernel Library Summary Statistics Application Notes document [SS Notes].

Parent topic: Summary Statistics Task Editors

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

vslSSEditRobustCovariance