novelist-package: NOVEL Integration of the Sample and Thresholded (NOVELIST)...
In novelist: NOVEL Integration of the Sample and Thresholded (NOVELIST) Correlation and Covariance Estimators
Description
Details
Author(s)
References
Examples
Description
Implements NOVELIST estimator,which is a nonlinear shrinkage estimator of the correlation and covariance matrices and their inverses. It performs shrinkage of the sample correlation matrix towards a thresholding target, yielding the NOVELIST correlation matrix estimator, and then obtain the corresponding NOVELIST covariance matrix estimator by applying the sample variances to the NOVELIST correlation matrix estimator. It also provide NOVELIST estimators of the correlation matrices and the inverse of the covariance/correlation matrices.
Details
Package: novelist
Type: Package
Version: 1.0
Date: 2015-05-12
License: GPL (>= 3)
The main routines of the package are novelist.cov.cv and novelist.inv.cv.
Author(s)
Na Huang and Piotr Fryzlewicz
Maintainer: Na Huang <n.huang1@lse.ac.uk>
References
Huang, N. & Fryzlewicz, P. (2015), "NOVELIST estimator of large correlation and covariance matrices and their inverses". Preprint.
Examples
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# arbitrary positive definite covariance matrix
cov.nonsparse<- function(p, rgen = rnorm, rgen.diag = rchisq, df = 5)
{
m <- matrix(rgen(p*p), p, p)
m[upper.tri(m)] <- 0
tmp <- m %*% t(m)
tmp.svd <- svd(tmp)
tmp.svd$d <- rgen.diag(p, df)
tmp.svd$u %*% diag(tmp.svd$d) %*% t(tmp.svd$u)
}
# simulate n x p data matrix by a given covariance matrix
sim.data <- function(sc, n, rgen = rnorm)
{
l <- t(chol(sc))
p <- dim(sc)[1]
z <- matrix(rgen(p * n), p, n)
t(l %*% z)
}
p=50
n=50
cov<-cov.nonsparse(p)
x<-sim.data(cov,n)
novelist.cov.cv(x, lambda=seq(0,1,by=0.1)) # NOVELIST estimator of the covariance matrix
novelist.inv.cv(x, lambda=seq(0,1,by=0.1)) # NOVELIST estimator of the precision matrix
Example output
[1] 1
[1] 2
[1] 3
[1] 4
[1] 5
[1] 6
[1] 7
[1] 8
[1] 9
[1] 10
[1] 11
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[1] 21
[1] 22
[1] 23
[1] 24
[1] 25
[1] 26
[1] 27
[1] 28
[1] 29
[1] 30
[1] 31
[1] 32
[1] 33
[1] 34
[1] 35
[1] 36
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[1] 38
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[1] 40
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[1] 45
[1] 46
[1] 47
[1] 48
[1] 49
[1] 50
$cov.novel
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[,11] [,12] [,13] [,14] [,15]
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[50,] 0.092343063 0.002254643 0.103928324 0.001959808 -0.506726050
[,16] [,17] [,18] [,19] [,20]
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[9,] 0.151579159 0.016496870 -0.201302517 0.247909751 0.51600463
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[20,] -0.416719470 -0.303338426 -0.240032032 -0.112244044 6.95361058
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[22,] 0.048298666 0.164472291 0.093812622 0.138997047 0.26917295
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$cor.novel
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$lambda.star
[1] 0.5
$delta.star
[1] 0.7492689
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[1] 5
[1] 6
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[1] 30
[1] 31
[1] 32
[1] 33
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[1] 35
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[1] 37
[1] 38
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[1] 40
[1] 41
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[1] 44
[1] 45
[1] 46
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[1] 48
[1] 49
[1] 50
$inv.cov.novel
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$inv.cor.novel
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[43,] -0.013462851 0.018803716 -0.035445920 -0.0112348082 0.0216833513
[44,] 0.069500826 -0.003958553 0.045714956 -0.0430563853 -0.0571668977
[45,] -0.026941562 0.037309379 0.027816747 0.0434753516 -0.0171845957
[46,] 1.071153397 0.054512053 -0.015262425 -0.0506831876 0.0428462633
[47,] 0.054512053 1.062730801 0.002946625 0.0209890271 -0.0702007162
[48,] -0.015262425 0.002946625 1.051677079 -0.0085532276 -0.0355382120
[49,] -0.050683188 0.020989027 -0.008553228 1.0725777390 0.0741165199
[50,] 0.042846263 -0.070200716 -0.035538212 0.0741165199 1.0818872019
$lambda.star
[1] 0.8
$delta.star
[1] 0.749381
novelist documentation built on May 30, 2017, 6:49 a.m.
R Package Documentation
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Description Details Author(s) References Examples
Description
Implements NOVELIST estimator,which is a nonlinear shrinkage estimator of the correlation and covariance matrices and their inverses. It performs shrinkage of the sample correlation matrix towards a thresholding target, yielding the NOVELIST correlation matrix estimator, and then obtain the corresponding NOVELIST covariance matrix estimator by applying the sample variances to the NOVELIST correlation matrix estimator. It also provide NOVELIST estimators of the correlation matrices and the inverse of the covariance/correlation matrices.
Details
| Package: | novelist |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2015-05-12 |
| License: | GPL (>= 3) |
The main routines of the package are novelist.cov.cv and novelist.inv.cv.
Author(s)
Na Huang and Piotr Fryzlewicz
Maintainer: Na Huang <n.huang1@lse.ac.uk>
References
Huang, N. & Fryzlewicz, P. (2015), "NOVELIST estimator of large correlation and covariance matrices and their inverses". Preprint.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 | # arbitrary positive definite covariance matrix
cov.nonsparse<- function(p, rgen = rnorm, rgen.diag = rchisq, df = 5)
{
m <- matrix(rgen(p*p), p, p)
m[upper.tri(m)] <- 0
tmp <- m %*% t(m)
tmp.svd <- svd(tmp)
tmp.svd$d <- rgen.diag(p, df)
tmp.svd$u %*% diag(tmp.svd$d) %*% t(tmp.svd$u)
}
# simulate n x p data matrix by a given covariance matrix
sim.data <- function(sc, n, rgen = rnorm)
{
l <- t(chol(sc))
p <- dim(sc)[1]
z <- matrix(rgen(p * n), p, n)
t(l %*% z)
}
p=50
n=50
cov<-cov.nonsparse(p)
x<-sim.data(cov,n)
novelist.cov.cv(x, lambda=seq(0,1,by=0.1)) # NOVELIST estimator of the covariance matrix
novelist.inv.cv(x, lambda=seq(0,1,by=0.1)) # NOVELIST estimator of the precision matrix
|
Example output
[1] 1
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[1] 47
[1] 48
[1] 49
[1] 50
$cov.novel
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[5,] -0.28952989 0.347666478 0.564757868 -0.194704510 4.4758322491
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[50,] -0.23489088 -0.043797598 0.441484270 -0.203091495 0.0056643355
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[6,] 4.9094872554 -0.16394052 0.20023342 -0.246104790 0.170636458
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[8,] 0.2002334250 -0.32665690 7.02369377 0.180402502 0.194713677
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[40,] 0.1741287586 -0.12377628 -0.15448597 0.334866262 -0.171967832
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[,11] [,12] [,13] [,14] [,15]
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[50,] 0.092343063 0.002254643 0.103928324 0.001959808 -0.506726050
[,16] [,17] [,18] [,19] [,20]
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[2,] 0.228920902 0.135259461 -0.067118530 -0.117668085 0.05022512
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[8,] 0.293385505 0.231809776 -0.520313546 -0.030729634 0.24577513
[9,] 0.151579159 0.016496870 -0.201302517 0.247909751 0.51600463
[10,] 0.129354433 -0.214156207 -0.002364748 0.051795015 -0.02840398
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[12,] -0.119755755 -0.002741883 -0.071360079 0.200050998 -0.25949235
[13,] -0.068990035 -0.205295846 -0.599366481 -0.083231196 0.45177463
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[16,] 5.732599072 0.016236422 0.011819068 0.346681258 -0.41671947
[17,] 0.016236422 5.802781851 0.132538630 0.310732887 -0.30333843
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[20,] -0.416719470 -0.303338426 -0.240032032 -0.112244044 6.95361058
[21,] -0.309765057 0.060011802 -0.288350162 -0.046137605 0.68817404
[22,] 0.048298666 0.164472291 0.093812622 0.138997047 0.26917295
[23,] 0.323341456 -0.038048430 -0.128945385 -0.311237369 -0.13500743
[24,] 0.073334254 0.042224255 -0.257792816 -0.093340958 0.20074173
[25,] -0.286001968 0.033570637 0.069251920 0.002622678 0.07678279
[26,] -0.229991652 -0.012293912 -0.051399840 -0.199059642 -0.34189433
[27,] 0.045832867 0.209609828 0.427638725 -0.217108156 -0.61541865
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$lambda.star
[1] 0.5
$delta.star
[1] 0.7492689
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[1] 50
$inv.cov.novel
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$inv.cor.novel
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[32,] 0.062251121 -0.043084617 -0.045437557 -0.0090783712 -0.0511631107
[33,] 0.012494539 -0.009743869 0.005124571 -0.0321533709 -0.0035232393
[34,] -0.022528274 0.037854096 -0.014468057 0.0053769540 0.0198507878
[35,] -0.007015989 -0.045003089 -0.009804127 0.0095397125 -0.0044367479
[36,] 0.057074826 -0.022156543 0.012178556 -0.0291728008 -0.0165344057
[37,] 0.057926834 -0.019058542 0.010007552 -0.0113522080 0.0781514941
[38,] 0.023060314 0.048554416 0.045061080 -0.0441325918 0.0240161511
[39,] -0.010514061 -0.003040202 0.028113881 0.0198115331 0.0328965262
[40,] -0.001717604 -0.038437219 0.044921183 -0.0439727725 0.0026687472
[41,] -0.024020933 -0.003546727 0.000680611 -0.0384182739 0.0064939449
[42,] -0.022008564 0.005209344 -0.036850561 0.0510826309 0.0024399343
[43,] -0.013462851 0.018803716 -0.035445920 -0.0112348082 0.0216833513
[44,] 0.069500826 -0.003958553 0.045714956 -0.0430563853 -0.0571668977
[45,] -0.026941562 0.037309379 0.027816747 0.0434753516 -0.0171845957
[46,] 1.071153397 0.054512053 -0.015262425 -0.0506831876 0.0428462633
[47,] 0.054512053 1.062730801 0.002946625 0.0209890271 -0.0702007162
[48,] -0.015262425 0.002946625 1.051677079 -0.0085532276 -0.0355382120
[49,] -0.050683188 0.020989027 -0.008553228 1.0725777390 0.0741165199
[50,] 0.042846263 -0.070200716 -0.035538212 0.0741165199 1.0818872019
$lambda.star
[1] 0.8
$delta.star
[1] 0.749381
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