Description Usage Arguments Details Value Author(s) References See Also Examples
Function that generates a (datadriven) default target for usage in (type I) ridge shrinkage estimation of the precision matrix (see ridgeP
).
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 ridgeP
).
1  default.target(S, type = "DAIE", fraction = 1e04, const)

S 
Sample covariance 
type 
A 
fraction 
A 
const 
A 
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.
The targets DUPV
, DCPV
, and Null
are not datadriven in the sense that the input matrix S
only provides information on the size of the desired target.
The targets DAIE
, DIAES
, DAPV
, and DEPV
are datadriven in the sense that the input matrix S
provides the information for the diagonal entries.
The argument fraction
is only used when type = "DAIE"
. The argument const
is only used when type = "DCPV"
.
All types except DEPV
and Null
lead to rotation equivariant alternative and archetypal Type I ridge estimators.
The target Null
also leads to a rotation equivariant alternative Type II ridge estimator (see ridgeP
).
Note that the DIAES
, DAPV
, and 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 matrix
.
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 HighDimensional Data, Computational Statistics & Data Analysis, vol. 103: 284303. Also available as arXiv:1403.0904v3 [stat.ME].
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