Ridge estimation for high-dimensional precision matrices with known sign of off-diagonal precision elements.

Function that calculates the ridge estimators for high-dimensional precision matrices with known sign of the off-diagonal precision elements.

ridgePsign(
  S,
  lambda,
  sign,
  target = default.target(S),
  type = "Alt",
  method = "nlm",
  verbose = TRUE,
  ...
)

Arguments

S

Sample covariance matrix.

lambda

A numeric representing the value of the penalty parameter.

sign

A character indicating the required sign of the off-diagonal elements of ridge precision estimate. Must be either: "pos" (positive) and "neg" (negative).

target

A target matrix (in precision terms) for the ridge precision estimator.

type

A character indicating the type of ridge estimator to be used. Must be one of: "Alt", "ArchI", "ArchII".

method

A character : which optimization function should be used: "nlm" (default) or "optim" which refer to nlminb or constrOptim, respectively.

verbose

Logical indicator: should intermediate output be printed on the screen?

...

Additional arguments passed on to either nlminb or constrOptim.

Value

The function returns a regularized precision matrix with off-diagonal elements of specified signed or zero.

Details

Modified version of the ridgePchordal-function, now the ridge precision matrix estimate has off-diagonal elements equalling zero or of the specified sign. The estimate is found by solving a constrained estimation problem. This is done numerically and employs the nlminb and constrOptim procedure of R. These procedures are initiated by the ridge ML precision estimate and its off-diagonal elements with the excluded sign set to (effectively) zero.

See also

ridgeP, ridgePchordal

Author

W.N. van Wieringen.

Examples

# obtain some data
p <- 8
n <- 100
set.seed(333)
Y <- matrix(rnorm(n*p), nrow = n, ncol = p)

# obtain regularized precision matrix with off-diagonal elements of specified signed
ridgePsign(covML(Y), lambda=0.1, sign="pos")
#>            [,1]    [,2]       [,3]       [,4]     [,5]       [,6]       [,7]
#> [1,] 1.10677331 0.00000 0.04470788 0.00000000 0.000000 0.01444850 0.00000000
#> [2,] 0.00000000 1.11899 0.00000000 0.00000000 0.000000 0.00000000 0.00000000
#> [3,] 0.04470788 0.00000 1.19493103 0.00000000 0.000000 0.13846365 0.17012323
#> [4,] 0.00000000 0.00000 0.00000000 0.95127218 0.000000 0.00000000 0.04376561
#> [5,] 0.00000000 0.00000 0.00000000 0.00000000 1.120341 0.00000000 0.00000000
#> [6,] 0.01444850 0.00000 0.13846365 0.00000000 0.000000 0.94358811 0.00000000
#> [7,] 0.00000000 0.00000 0.17012323 0.04376561 0.000000 0.00000000 1.29009913
#> [8,] 0.00000000 0.00000 0.16437939 0.05358874 0.000000 0.08897917 0.01493089
#>            [,8]
#> [1,] 0.00000000
#> [2,] 0.00000000
#> [3,] 0.16437939
#> [4,] 0.05358874
#> [5,] 0.00000000
#> [6,] 0.08897917
#> [7,] 0.01493089
#> [8,] 0.94072961