bandingEst()
estimates the covariance matrix of data with
ordered variables by forcing off-diagonal entries to be zero for indices
that are far removed from one another. The i, j entry of the estimated
covariance matrix will be zero if the absolute value of i - j is greater
than some non-negative constant k
. This estimator was proposed by
Bickel and Levina (2008)
.
bandingEst(dat, k)
dat | A numeric |
---|---|
k | A non-negative, |
A matrix
corresponding to the estimate of the covariance
matrix.
Bickel PJ, Levina E (2008). “Regularized estimation of large covariance matrices.” Annals of Statistics, 36(1), 199--227. doi: 10.1214/009053607000000758 , https://doi.org/10.1214/009053607000000758.
bandingEst(dat = mtcars, k = 2L)#> [,1] [,2] [,3] [,4] [,5] [,6] #> [1,] 36.324103 -9.172379 -633.09721 0.00000 0.00000000 0.0000000 #> [2,] -9.172379 3.189516 199.66028 101.93145 0.00000000 0.0000000 #> [3,] -633.097208 199.660282 15360.79983 6721.15867 -47.06401915 0.0000000 #> [4,] 0.000000 101.931452 6721.15867 4700.86694 -16.45110887 44.1926613 #> [5,] 0.000000 0.000000 -47.06402 -16.45111 0.28588135 -0.3727207 #> [6,] 0.000000 0.000000 0.00000 44.19266 -0.37272073 0.9573790 #> [7,] 0.000000 0.000000 0.00000 0.00000 0.08714073 -0.3054816 #> [8,] 0.000000 0.000000 0.00000 0.00000 0.00000000 -0.2736613 #> [9,] 0.000000 0.000000 0.00000 0.00000 0.00000000 0.0000000 #> [10,] 0.000000 0.000000 0.00000 0.00000 0.00000000 0.0000000 #> [11,] 0.000000 0.000000 0.00000 0.00000 0.00000000 0.0000000 #> [,7] [,8] [,9] [,10] [,11] #> [1,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [2,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [3,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [4,] 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000 #> [5,] 0.08714073 0.00000000 0.00000000 0.0000000 0.00000000 #> [6,] -0.30548161 -0.27366129 0.00000000 0.0000000 0.00000000 #> [7,] 3.19316613 0.67056452 -0.20495968 0.0000000 0.00000000 #> [8,] 0.67056452 0.25403226 0.04233871 0.0766129 0.00000000 #> [9,] -0.20495968 0.04233871 0.24899194 0.2923387 0.04637097 #> [10,] 0.00000000 0.07661290 0.29233871 0.5443548 0.32661290 #> [11,] 0.00000000 0.00000000 0.04637097 0.3266129 2.60887097