indx_Commutator_Moment {MultiStatM}R Documentation

Linear combination of moments

Description

For a d-variate distribution it provides the product Kx where K is the moment commutator as produced by matr_Commutator_Moment and x is a vector of appropriate dimension. It avoids the construction of large commutators matrices working much faster with respect to matr_Commutator_Moment.

Usage

indx_Commutator_Moment(x, el_rm, d)

Arguments

x

a vector of length d^n where n is length of (el_rm)

el_rm

type of a partition

d

dimensionality of the underlying multivariate distribution

Value

A vector K x

References

Gy., Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021, Section 2.4.3, p.100, Sect. A.2.1, p. 353., Corollary 2.6., p.95

See Also

Other Matrices and commutators: indx_Commutator_Kmn(), indx_Commutator_Kperm(), indx_Commutator_Mixing(), indx_Elimination(), indx_Qplication(), indx_Symmetry(), indx_UnivMomCum(), matr_Commutator_Kmn(), matr_Commutator_Kperm(), matr_Commutator_Mixing(), matr_Commutator_Moment(), matr_Elimination(), matr_Qplication(), matr_Symmetry()

Examples

n=4;  r=2 ;  m=1 ;  d=2;
PTA<-Partition_Type_All(n)
el_r<-PTA$eL_r[[r]][m,]
## el_r is a given type (always a vector)
x<-1:d^n
indx_Commutator_Moment(x,el_r,d)
# Same as
MC<- matr_Commutator_Moment(el_r,d)
as.vector(MC%*%x)

[Package MultiStatM version 1.2.1 Index]