Expected hessian of a parametric S-vine models
svine_hessian(x, model, cores = 1)the data.
S-vine model (inheriting from svine_dist).
number of cores to use.
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.
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 -7.272346e-08 1.251305e-06 -1.910311e-07 -1.168358e-05
#> [2,] -7.272346e-08 2.742702e-07 -9.648874e-08 1.579411e-07 1.498636e-06
#> [3,] 1.251305e-06 -9.648874e-08 2.312842e-06 -2.382406e-07 2.483107e-05
#> [4,] -1.910311e-07 1.579411e-07 -2.382406e-07 3.800397e-07 -6.936534e-06
#> [5,] -1.168358e-05 1.498636e-06 2.483107e-05 -6.936534e-06 2.901260e-03
#> [6,] 7.321560e-05 1.461359e-04 2.460298e-04 1.070328e-04 2.775175e-02
#> [7,] 2.201479e-05 3.191181e-08 2.451189e-06 -4.426845e-08 5.152500e-04
#> [8,] -5.200381e-04 2.666284e-04 -5.876481e-04 -4.609263e-06 -1.562355e-02
#> [9,] 2.009948e-05 6.246524e-07 1.157621e-05 1.257099e-05 -1.267362e-03
#> [,6] [,7] [,8] [,9]
#> [1,] 0.0000732156 2.201479e-05 -5.200381e-04 2.009948e-05
#> [2,] 0.0001461359 3.191181e-08 2.666284e-04 6.246524e-07
#> [3,] 0.0002460298 2.451189e-06 -5.876481e-04 1.157621e-05
#> [4,] 0.0001070328 -4.426845e-08 -4.609263e-06 1.257099e-05
#> [5,] 0.0277517462 5.152500e-04 -1.562355e-02 -1.267362e-03
#> [6,] 2.4984113779 2.507666e-02 -5.657979e-02 1.999937e-02
#> [7,] 0.0250766551 1.281737e-02 -1.078909e-01 8.848302e-04
#> [8,] -0.0565797906 -1.078909e-01 6.793559e+00 -1.017606e-02
#> [9,] 0.0199993676 8.848302e-04 -1.017606e-02 9.022121e-03