
Qualitative correlation or covariance kernel with one input and low-rank correlation.
q1LowRank(factor, rank = 2L, input = "x",
cov = c("corr", "homo", "hete"), intAsChar = TRUE)
An object with class "covQual"
with d = 1
qualitative
input.
A factor with the wanted levels for the covariance kernel object.
The wanted rank, which must be
Name of (qualitative) input for the kernel.
Character telling what variance structure will be chosen:
correlation with no variance parameter, homoscedastic
with one variance parameter or heteroscedastic with
Logical. If TRUE
(default), an integer-valued input will be
coerced into a character. Otherwise, it will be coerced into a factor.
The correlation structure involves
Correlation kernels are needed in tensor products because the tensor product of two covariance kernels each with unknown variance would not be identifiable.
Francesco Rapisarda, Damanio Brigo, Fabio Mercurio (2007). "Parameterizing Correlations a Geometric Interpretation". IMA Journal of Management Mathematics, 18(1): 55-73.
Igor Grubišić, Raoul Pietersz (2007). "Efficient Rank Reduction of Correlation Matrices". Linear Algebra and its Applications, 422: 629-653.
The q1Symm
function to create a kernel object for the
full-rank case and corLevLowRank
for the correlation
function.
myFact <- factor(letters[1:8])
myCov <- q1LowRank(factor = myFact, rank = 3)
## corrplot
plot(myCov)
## find the rank using a pivoted Cholesky
chol(covMat(myCov), pivot = TRUE)
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