Koden for normindex

computeNormIndex
## function (my.data) 
## {
##     my.data <- data.frame(my.data)
##     d <- ncol(my.data)
##     indices <- NULL
##     for (i2 in 1:(d - 1)) {
##         for (i1 in (i2 + 1):d) {
##             indices <- rbind(indices, c(i1, i2))
##         }
##     }
##     Tstat <- nrow(my.data) * computeT(my.data, indices)
##     vd <- getVd.sam(my.data)
##     alphas <- eigen(vd)$values
##     alphas <- alphas[alphas > 1e-05]
##     normindex <- (Tstat - sum(alphas))/sqrt((2 * sum(alphas^2)))
##     return(normindex)
## }

Design

Underlying correlation matrix \(p=5\): And \(p=10\)

We simulated 30 samples in each conditions.

Results

Index increases moderately with dimension.

## # A tibble: 6 x 4
## # Groups:   p [2]
##       p variable       mean    sd
##   <dbl> <fct>         <dbl> <dbl>
## 1     5 normal      -0.0367 0.865
## 2     5 vitaclayton  3.36   2.61 
## 3     5 vitajoe      5.54   3.58 
## 4    10 normal       0.0128 0.726
## 5    10 vitaclayton  4.42   3.72 
## 6    10 vitajoe      6.12   4.75

Index increases with sample size

## # A tibble: 6 x 4
## # Groups:   n [2]
##       n variable       mean    sd
##   <dbl> <fct>         <dbl> <dbl>
## 1   500 normal       0.0377 0.741
## 2   500 vitaclayton  2.36   1.81 
## 3   500 vitajoe      3.67   2.49 
## 4  1000 normal      -0.0616 0.850
## 5  1000 vitaclayton  5.41   3.64 
## 6  1000 vitajoe      7.99   4.47

Index decreases with \(K\)

## # A tibble: 9 x 4
## # Groups:   k [3]
##       k variable        mean    sd
##   <dbl> <fct>          <dbl> <dbl>
## 1     3 normal      -0.00558 0.972
## 2     3 vitaclayton  6.94    3.79 
## 3     3 vitajoe     10.0     4.45 
## 4     7 normal      -0.0453  0.791
## 5     7 vitaclayton  2.82    1.44 
## 6     7 vitajoe      4.52    2.02 
## 7    10 normal       0.0150  0.589
## 8    10 vitaclayton  1.91    0.984
## 9    10 vitajoe      2.98    1.46

Index higher under Joe Vita compared to Clayton vita

## # A tibble: 3 x 3
##   variable       mean    sd
##   <fct>         <dbl> <dbl>
## 1 normal      -0.0120 0.798
## 2 vitaclayton  3.89   3.25 
## 3 vitajoe      5.83   4.21