MultiStatM (version 2.0.0)

SymMatr: Symmetrizer Matrix

Description

Based on Chacon and Duong (2015) efficient recursive algorithms for functionals based on higher order derivatives. An option for sparse matrix is provided. By using sparse matrices far less memory is required and faster computation times are obtained

Usage

SymMatr(d, n, useSparse = FALSE)

Value

A Symmetrizer matrix with order \({d^n} \times d^n\). If useSparse=TRUE

an object of the class "dgCMatrix" is produced.

Arguments

d

dimension of a vector x

n

power of the Kronecker product

useSparse

TRUE or FALSE. If TRUE an object of the class "dgCMatrix" is produced.

References

Chacon, J. E., and Duong, T. (2015). Efficient recursive algorithms for functionals based on higher order derivatives of the multivariate Gaussian density. Statistics and Computing, 25(5), 959-974.

Gy. Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021.Section 1.3.1 Symmetrization, p.14. (1.29)

See Also

Other Matrices and commutators: EliminIndx(), EliminMatr(), QplicIndx(), QplicMatr(), SymIndx(), UnivMomCum()

Examples

a<-c(1,2)
b<-c(2,3)
c<-kronecker(kronecker(a,a),b)
## The symmetrized version of c is
as.vector(SymMatr(2,3)%*%c)