ElliptCopulas (version 0.1.4.1)

compute_matrix_alpha: Compute the matrix of coefficients alpha

Description

This matrix of coefficient is useful for the estimation of higher-order derivatives of an elliiptical distribution density generator. It is introduced in Section 3 of (Ryan and Derumigny, 2024).

Usage

compute_matrix_alpha(kmax, grid, a, d)

Value

a (kmax+1) * (kmax+1) * length(grid) array

Arguments

kmax

order the derivative that we want to compute

grid

the grid of the values at which we want to compute the derivative

a

the tuning parameter controlling the bias of the estimator at zero.

d

the dimension of the problem

Author

Victor Ryan, Alexis Derumigny

References

Ryan, V., & Derumigny, A. (2024). On the choice of the two tuning parameters for nonparametric estimation of an elliptical distribution generator arxiv:2408.17087.

See Also

This function uses the internal functions derivative.tau and derivative.psi. See also vectorized_Faa_di_Bruno.

Examples

kmax = 1
d = 3
grid = 0.2
a = 0.8
compute_matrix_alpha(kmax = kmax, grid = grid, a = a, d = d)