Hermite_Poly_NH_Multi_Inv {MultiStatM}R Documentation

Inverse of d-variate T-Hermite Polynomial

Description

Compute the powers of vector variate x when Hermite polynomials are given

Usage

Hermite_Poly_NH_Multi_Inv(H_N_X, N, Sig2 = diag(length(H_N_X[[1]])))

Arguments

H_N_X

The list of d-variate T-Hermite Polynomials of order from 1 to N evaluated at X

N

the highest polynomial order

Sig2

The variance matrix of x, the default is set to unit matrix

Value

The list of x, x^{\otimes 2},... x^{\otimes N}

References

Gy.Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021. Section 4.6.2, (4.72), p.223

See Also

Other Hermite: Hermite_CoeffMulti(), Hermite_Coeff(), Hermite_N_Cov_X1_X2(), Hermite_Nth(), Hermite_Poly_HN_Multi(), Hermite_Poly_HN(), Hermite_Poly_NH_Inv()

Examples

x<-c(1,3)
Sig2 <- diag(length(x)) # matrix(c(1,0,0,1),2,2,byrow=T)
N<-4
H_N_X<-Hermite_Poly_HN_Multi(x,N,Sig2)
x_ad_n <- Hermite_Poly_NH_Multi_Inv(H_N_X,N,Sig2)

[Package MultiStatM version 1.2.1 Index]