Expected hessian of a parametric S-vine models
Arguments
- x
the data.
- model
S-vine model (inheriting from svine_dist).
- cores
number of cores to use.
Value
A returns a k-by-k matrix, where k is the
total number of parameters in the
model. Parameters are ordered as follows:
marginal parameters, copula parameters of first tree, copula parameters of
second tree, etc. Duplicated parameters in the copula model are omitted.
Examples
data(returns)
dat <- returns[1:100, 1:2]
# fit parametric S-vine model with Markov order 1
model <- svine(dat, p = 1, family_set = "parametric")
# Implementation of asymptotic variances
I <- cov(svine_scores(dat, model))
H <- svine_hessian(dat, model)
Hi <- solve(H)
Hi %*% I %*% t(Hi) / nrow(dat)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.646796e-06 -7.272345e-08 1.251305e-06 -1.910311e-07 -1.168358e-05
#> [2,] -7.272345e-08 2.742702e-07 -9.648873e-08 1.579411e-07 1.498636e-06
#> [3,] 1.251305e-06 -9.648873e-08 2.312842e-06 -2.382406e-07 2.483107e-05
#> [4,] -1.910311e-07 1.579411e-07 -2.382406e-07 3.800397e-07 -6.936533e-06
#> [5,] -1.168358e-05 1.498636e-06 2.483107e-05 -6.936533e-06 2.901260e-03
#> [6,] 7.321565e-05 1.461360e-04 2.460297e-04 1.070329e-04 2.775175e-02
#> [7,] 2.201479e-05 3.191346e-08 2.451188e-06 -4.426826e-08 5.152500e-04
#> [8,] -5.200379e-04 2.666283e-04 -5.876480e-04 -4.609253e-06 -1.562354e-02
#> [9,] 2.009948e-05 6.246523e-07 1.157621e-05 1.257099e-05 -1.267362e-03
#> [,6] [,7] [,8] [,9]
#> [1,] 7.321565e-05 2.201479e-05 -5.200379e-04 2.009948e-05
#> [2,] 1.461360e-04 3.191346e-08 2.666283e-04 6.246523e-07
#> [3,] 2.460297e-04 2.451188e-06 -5.876480e-04 1.157621e-05
#> [4,] 1.070329e-04 -4.426826e-08 -4.609253e-06 1.257099e-05
#> [5,] 2.775175e-02 5.152500e-04 -1.562354e-02 -1.267362e-03
#> [6,] 2.498412e+00 2.507666e-02 -5.657978e-02 1.999937e-02
#> [7,] 2.507666e-02 1.281737e-02 -1.078908e-01 8.848303e-04
#> [8,] -5.657978e-02 -1.078908e-01 6.793555e+00 -1.017606e-02
#> [9,] 1.999937e-02 8.848303e-04 -1.017606e-02 9.022121e-03