Hermite_Poly_NH_Multi_Inv {MultiStatM} | R Documentation |
Compute the powers of vector variate x when Hermite polynomials are given
Hermite_Poly_NH_Multi_Inv(H_N_X, N, Sig2 = diag(length(H_N_X[[1]])))
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 |
The list of x
, x^{\otimes 2}
,... x^{\otimes N}
Gy.Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021. Section 4.6.2, (4.72), p.223
Other Hermite:
Hermite_CoeffMulti()
,
Hermite_Coeff()
,
Hermite_N_Cov_X1_X2()
,
Hermite_Nth()
,
Hermite_Poly_HN_Multi()
,
Hermite_Poly_HN()
,
Hermite_Poly_NH_Inv()
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)