This function is now deprecated. Please use ridgeP instead.
ridgeS(S, lambda, type = "Alt", target = default.target(S))Sample covariance matrix.
A numeric representing the value of the penalty
parameter.
A character indicating the type of ridge estimator to be
used. Must be one of: "Alt", "ArchI", "ArchII".
A target matrix (in precision terms) for Type I ridge
estimators.
Function returns a regularized precision matrix.
See ridgeP.
## Obtain some (high-dimensional) data
p = 25
n = 10
set.seed(333)
X = matrix(rnorm(n*p), nrow = n, ncol = p)
colnames(X)[1:25] = letters[1:25]
Cx <- covML(X)
## Obtain regularized precision matrix
ridgeS(Cx, lambda = 10, type = "Alt")
#> Warning: This function is deprecated. Please use ridgeP instead.
#> a b c d e
#> a 0.7586005611 -3.388106e-03 -0.062306628 -0.0026003511 0.017829395
#> b -0.0033881061 8.242435e-01 -0.020123673 -0.0086472201 -0.031021296
#> c -0.0623066280 -2.012367e-02 0.764718837 -0.0387376011 0.026085391
#> d -0.0026003511 -8.647220e-03 -0.038737601 0.8175180716 0.025132790
#> e 0.0178293946 -3.102130e-02 0.026085391 0.0251327896 0.774812407
#> f 0.0008224896 7.036266e-03 0.016128380 0.0022115795 -0.007716194
#> g 0.0239384853 2.987486e-02 -0.012622966 -0.0372816975 0.062273754
#> h -0.0184532319 -2.016088e-02 -0.017811658 0.0111872795 -0.005983202
#> i -0.0470808853 -1.320536e-03 -0.050429118 -0.0102469052 -0.005016085
#> j 0.0104108210 1.273107e-02 0.041011188 0.0004608857 0.012722811
#> k -0.0131022276 2.557898e-02 0.020638624 0.0126209008 0.050816129
#> l 0.0277590914 -2.068251e-03 0.006432918 0.0140749509 -0.015112009
#> m -0.0020174916 2.716174e-03 -0.019386166 0.0215940085 -0.028209810
#> n -0.0050899852 -3.421883e-02 0.028203144 0.0374757352 -0.058307497
#> o -0.0298904142 -1.737302e-03 -0.033993574 -0.0067855046 0.023577321
#> p -0.0135277622 1.138140e-02 0.012192115 -0.0041639552 0.036093905
#> q 0.0551271528 2.630552e-02 0.047234421 0.0041346960 0.033640610
#> r -0.0409270257 1.074517e-02 -0.037103191 -0.0067177023 0.033946832
#> s 0.0187078578 9.049344e-05 -0.020540566 -0.0284800378 0.022291853
#> t -0.0037077889 -1.690321e-02 -0.014231135 -0.0024523956 -0.018163057
#> u -0.0198084868 -8.668786e-04 -0.034835952 -0.0118549709 0.027191508
#> v -0.0335506701 -2.568611e-02 -0.067083077 -0.0323202749 0.035487211
#> w 0.0157456815 2.298104e-02 0.010338930 0.0038751229 0.012513934
#> x 0.0292757599 4.649014e-03 0.006331822 0.0273137627 -0.014949799
#> y 0.0070194748 1.148079e-03 0.009556118 0.0140203937 -0.012091685
#> f g h i j
#> a 0.0008224896 0.023938485 -0.018453232 -0.0470808853 0.0104108210
#> b 0.0070362659 0.029874865 -0.020160876 -0.0013205357 0.0127310720
#> c 0.0161283801 -0.012622966 -0.017811658 -0.0504291179 0.0410111882
#> d 0.0022115795 -0.037281697 0.011187280 -0.0102469052 0.0004608857
#> e -0.0077161936 0.062273754 -0.005983202 -0.0050160851 0.0127228115
#> f 0.8303406862 -0.027948754 -0.001694060 -0.0008401972 -0.0042258829
#> g -0.0279487543 0.730220491 -0.007778146 0.0046553159 0.0229314532
#> h -0.0016940600 -0.007778146 0.811790777 -0.0016188175 0.0334725837
#> i -0.0008401972 0.004655316 -0.001618817 0.8112361283 0.0281494771
#> j -0.0042258829 0.022931453 0.033472584 0.0281494771 0.8030401602
#> k -0.0185728401 -0.035677847 -0.012348125 0.0253943227 -0.0251907952
#> l 0.0023936548 0.002304446 0.001210866 0.0008949424 0.0220445024
#> m -0.0018737321 0.009864846 -0.004756187 -0.0313568497 0.0448545754
#> n 0.0168437455 0.068879430 -0.047938427 0.0277609348 0.0043522696
#> o 0.0147906192 0.016179835 0.004670393 -0.0058931715 -0.0037850078
#> p 0.0008642891 -0.034133310 -0.017715835 0.0070383765 -0.0058047255
#> q -0.0185548657 -0.032054257 0.022673030 0.0251858785 -0.0368767434
#> r -0.0052481289 -0.002607246 0.012193002 -0.0236799071 -0.0032747580
#> s -0.0004541730 -0.060722864 -0.004402116 -0.0028112502 0.0260398598
#> t -0.0105699848 -0.009197778 -0.026308197 0.0011667515 0.0179069907
#> u 0.0183676161 0.013238884 0.010435589 0.0016139404 -0.0078895059
#> v 0.0397788162 0.016005142 -0.009825413 -0.0095763668 0.0090720048
#> w -0.0368897092 -0.035477080 0.014557746 -0.0056232667 -0.0092374685
#> x -0.0014562788 0.010277123 0.007403657 -0.0012875400 0.0246045874
#> y -0.0100608024 0.009426456 0.017442178 0.0007104261 0.0052519063
#> k l m n o
#> a -0.0131022276 0.0277590914 -0.0020174916 -0.005089985 -0.029890414
#> b 0.0255789789 -0.0020682507 0.0027161744 -0.034218827 -0.001737302
#> c 0.0206386237 0.0064329182 -0.0193861661 0.028203144 -0.033993574
#> d 0.0126209008 0.0140749509 0.0215940085 0.037475735 -0.006785505
#> e 0.0508161286 -0.0151120086 -0.0282098101 -0.058307497 0.023577321
#> f -0.0185728401 0.0023936548 -0.0018737321 0.016843745 0.014790619
#> g -0.0356778467 0.0023044464 0.0098648456 0.068879430 0.016179835
#> h -0.0123481250 0.0012108659 -0.0047561873 -0.047938427 0.004670393
#> i 0.0253943227 0.0008949424 -0.0313568497 0.027760935 -0.005893171
#> j -0.0251907952 0.0220445024 0.0448545754 0.004352270 -0.003785008
#> k 0.7919840968 0.0145247777 0.0267107840 0.009680268 -0.007959987
#> l 0.0145247777 0.8281242740 -0.0393495308 0.017837074 0.001717317
#> m 0.0267107840 -0.0393495308 0.7921869253 0.019705584 -0.003267645
#> n 0.0096802678 0.0178370735 0.0197055844 0.722693528 0.011566322
#> o -0.0079599867 0.0017173170 -0.0032676445 0.011566322 0.831133082
#> p -0.0289796530 0.0232900959 0.0417812937 -0.008226868 0.017578383
#> q -0.0403380771 -0.0115900459 0.0127985120 0.061999123 0.013663539
#> r -0.0206727117 -0.0054939353 -0.0181878881 0.059407408 -0.031004871
#> s 0.0080620186 -0.0085836621 -0.0011216986 0.034433413 0.007897329
#> t 0.0006461893 0.0049746259 -0.0045811257 -0.032851992 0.001310240
#> u -0.0071545162 0.0018665882 -0.0009302928 0.012171909 -0.039476483
#> v 0.0114430467 0.0096174706 0.0168930005 -0.001362309 -0.038506838
#> w -0.0301450863 -0.0143661301 -0.0253453570 0.065639858 0.001297911
#> x 0.0075322245 -0.0558881608 -0.0663671412 0.038799832 -0.009921826
#> y 0.0028295809 -0.0369055638 -0.0367185905 0.040816631 -0.008922838
#> p q r s t
#> a -0.0135277622 0.055127153 -0.040927026 1.870786e-02 -0.0037077889
#> b 0.0113814004 0.026305523 0.010745169 9.049344e-05 -0.0169032091
#> c 0.0121921153 0.047234421 -0.037103191 -2.054057e-02 -0.0142311346
#> d -0.0041639552 0.004134696 -0.006717702 -2.848004e-02 -0.0024523956
#> e 0.0360939054 0.033640610 0.033946832 2.229185e-02 -0.0181630567
#> f 0.0008642891 -0.018554866 -0.005248129 -4.541730e-04 -0.0105699848
#> g -0.0341333099 -0.032054257 -0.002607246 -6.072286e-02 -0.0091977785
#> h -0.0177158353 0.022673030 0.012193002 -4.402116e-03 -0.0263081972
#> i 0.0070383765 0.025185879 -0.023679907 -2.811250e-03 0.0011667515
#> j -0.0058047255 -0.036876743 -0.003274758 2.603986e-02 0.0179069907
#> k -0.0289796530 -0.040338077 -0.020672712 8.062019e-03 0.0006461893
#> l 0.0232900959 -0.011590046 -0.005493935 -8.583662e-03 0.0049746259
#> m 0.0417812937 0.012798512 -0.018187888 -1.121699e-03 -0.0045811257
#> n -0.0082268677 0.061999123 0.059407408 3.443341e-02 -0.0328519922
#> o 0.0175783825 0.013663539 -0.031004871 7.897329e-03 0.0013102396
#> p 0.7937112327 -0.010501867 0.016366395 -1.453934e-02 0.0147201267
#> q -0.0105018671 0.757364872 -0.015103087 -1.108296e-03 0.0247241993
#> r 0.0163663948 -0.015103087 0.807436924 5.143353e-03 0.0110409176
#> s -0.0145393446 -0.001108296 0.005143353 8.220992e-01 -0.0014786838
#> t 0.0147201267 0.024724199 0.011040918 -1.478684e-03 0.8315488933
#> u 0.0281843153 0.013628334 -0.029953009 6.678695e-03 -0.0023284664
#> v -0.0024803522 0.031688866 -0.019089549 -1.096010e-02 0.0013064244
#> w 0.0275664464 -0.063035943 -0.036020971 2.733150e-03 -0.0023237007
#> x 0.0487962438 -0.025856194 -0.028478077 -5.798014e-04 0.0075267137
#> y 0.0303086817 -0.010854167 -0.029443191 -7.038769e-04 0.0131367455
#> u v w x y
#> a -0.0198084868 -0.033550670 0.0157456815 0.0292757599 0.0070194748
#> b -0.0008668786 -0.025686113 0.0229810411 0.0046490144 0.0011480793
#> c -0.0348359521 -0.067083077 0.0103389296 0.0063318217 0.0095561180
#> d -0.0118549709 -0.032320275 0.0038751229 0.0273137627 0.0140203937
#> e 0.0271915077 0.035487211 0.0125139342 -0.0149497995 -0.0120916851
#> f 0.0183676161 0.039778816 -0.0368897092 -0.0014562788 -0.0100608024
#> g 0.0132388837 0.016005142 -0.0354770805 0.0102771226 0.0094264560
#> h 0.0104355893 -0.009825413 0.0145577461 0.0074036567 0.0174421783
#> i 0.0016139404 -0.009576367 -0.0056232667 -0.0012875400 0.0007104261
#> j -0.0078895059 0.009072005 -0.0092374685 0.0246045874 0.0052519063
#> k -0.0071545162 0.011443047 -0.0301450863 0.0075322245 0.0028295809
#> l 0.0018665882 0.009617471 -0.0143661301 -0.0558881608 -0.0369055638
#> m -0.0009302928 0.016893000 -0.0253453570 -0.0663671412 -0.0367185905
#> n 0.0121719092 -0.001362309 0.0656398583 0.0387998319 0.0408166311
#> o -0.0394764835 -0.038506838 0.0012979109 -0.0099218258 -0.0089228384
#> p 0.0281843153 -0.002480352 0.0275664464 0.0487962438 0.0303086817
#> q 0.0136283336 0.031688866 -0.0630359426 -0.0258561943 -0.0108541671
#> r -0.0299530088 -0.019089549 -0.0360209711 -0.0284780774 -0.0294431907
#> s 0.0066786951 -0.010960102 0.0027331505 -0.0005798014 -0.0007038769
#> t -0.0023284664 0.001306424 -0.0023237007 0.0075267137 0.0131367455
#> u 0.8144249032 -0.044021397 -0.0001474572 -0.0114020196 -0.0068419484
#> v -0.0440213967 0.777514000 0.0413707831 0.0163870077 0.0151914605
#> w -0.0001474572 0.041370783 0.7818068418 -0.0417448243 -0.0263768835
#> x -0.0114020196 0.016387008 -0.0417448243 0.7686584964 -0.0648558659
#> y -0.0068419484 0.015191461 -0.0263768835 -0.0648558659 0.7975906091