The population model

The vita distribution and the thresholds

The vita distribution consists of mostly joe copulas. The first two vine trees:

We found some thresholds were the default nt approach seemed to perform poorly.

For k=7

For k=10

Bootstrap SEs versus the default NT SEs

The simulation design crossed two sample sizes \(n=500,1000\) with two thresholds \(k=7, 10\). In each condition 500 discrete samples were generated. From each discrete sample, 1000 bootstrap samples were drawn.

Summaries across parameters, with absolute RB in the second table:

## # A tibble: 4 x 4
## # Groups:   n [2]
##       n k      rbboot rbdefault
##   <dbl> <fct>   <dbl>     <dbl>
## 1   500 7     -0.465      -12.0
## 2   500 10    -0.0575     -14.9
## 3  1000 7     -2.79       -12.3
## 4  1000 10    -1.68       -14.4
## # A tibble: 4 x 4
## # Groups:   n [2]
##       n k     ABSrbboot ABSrbdefault
##   <dbl> <fct>     <dbl>        <dbl>
## 1   500 7          3.11         12.0
## 2   500 10         2.83         14.9
## 3  1000 7          3.11         12.3
## 4  1000 10         3.40         14.4

Coverage

Overall coverage

## # A tibble: 4 x 2
##   method          `mean(covered)`
##   <fct>                     <dbl>
## 1 boot.percentile           0.848
## 2 default                   0.794
## 3 boot.z                    0.848
## 4 boot.bc                   0.841

And further subdivided

## # A tibble: 16 x 4
## # Groups:   n, k [4]
##        n     k method          `mean(covered)`
##    <dbl> <dbl> <fct>                     <dbl>
##  1   500     7 boot.percentile           0.848
##  2   500     7 default                   0.793
##  3   500     7 boot.z                    0.849
##  4   500     7 boot.bc                   0.835
##  5   500    10 boot.percentile           0.92 
##  6   500    10 default                   0.867
##  7   500    10 boot.z                    0.920
##  8   500    10 boot.bc                   0.917
##  9  1000     7 boot.percentile           0.735
## 10  1000     7 default                   0.682
## 11  1000     7 boot.z                    0.734
## 12  1000     7 boot.bc                   0.725
## 13  1000    10 boot.percentile           0.889
## 14  1000    10 default                   0.836
## 15  1000    10 boot.z                    0.888
## 16  1000    10 boot.bc                   0.887

Plots for each parameter: