derivative.rho {ElliptCopulas} | R Documentation |
Computing \rho
and its k
-th derivative
Description
The function \rho
is used to compute \widetilde{AMSE}
.
The quantity \widetilde{AMSE}
is of interest
because we can use it to find the optimal a
.
Usage
derivative.rho(grid, a, d, k, derivatives.g)
Arguments
grid |
a grid of numeric values |
a |
a parameter |
d |
the dimension of the data |
k |
the order of derivative of |
derivatives.g |
a matrix of size |
Value
a numeric vector \rho(grid[1])^{(k)}, \dots, \rho(grid[N])^{(k)}
,
where N
is the length of the grid
Author(s)
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
derivative.tau
and derivative.psi
.
EllDistrDerivEst
for the nonparametric estimation of the derivatives
of g
, the elliptical distribution density generator.
compute_matrix_alpha
which is used for the computation
of the derivatives.
Examples
# Return the 5-th derivative of tau at x = 1
grid = c(1)
a = 1; d = 3; k = 3
der.g = matrix(seq(1, 3, length.out = 4), nrow = 1)
derivative.rho(grid = grid, a = a, d = d, k = k, derivatives.g = der.g)