Function that generates a (data-driven) default target for usage in (type I) ridge shrinkage estimation of the precision matrix (see
The target that is generated is to be understood in precision terms.
Most options for target generation result in a target that implies a situation of rotation equivariant estimation (see
The function can generate the following default target matrices:
DAIE: Diagonal matrix with average of inverse nonzero eigenvalues of S as entries;
DIAES: Diagonal matrix with inverse of average of eigenvalues of S as entries;
DUPV: Diagonal matrix with unit partial variance as entries (identity matrix);
DAPV: Diagonal matrix with average of inverse variances of
S as entries;
DCPV: Diagonal matrix with constant partial variance as entries. Allows one to use other constant than DAIE, DIAES, DUPV, DAPV, and in a sense Null;
DEPV: Diagonal matrix with the inverse variances of
S as entries;
Null: Null matrix.
Null are not data-driven in the sense that the input matrix
S only provides information on the size of the desired target.
DEPV are data-driven in the sense that the input matrix
S provides the information for the diagonal entries.
fraction is only used when
type = "DAIE". The argument
const is only used when
type = "DCPV".
All types except
Null lead to rotation equivariant alternative and archetypal Type I ridge estimators.
Null also leads to a rotation equivariant alternative Type II ridge estimator (see
Note that the
DEPV targets amount to the identity matrix when the sample covariance matrix
S is standardized to be the correlation matrix.
The same goes, naturally, for the
DCPV target when
const is specified to be 1.
Function returns a target
Carel F.W. Peeters <[email protected]>, Wessel N. van Wieringen
van Wieringen, W.N. & Peeters, C.F.W. (2016). Ridge Estimation of Inverse Covariance Matrices from High-Dimensional Data, Computational Statistics & Data Analysis, vol. 103: 284-303. Also available as arXiv:1403.0904v3 [stat.ME].
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