# Aurora

`Aurora.AuroraKNN`

— Type```
AuroraKNN(;kKNN=1000, loocv=true, tree=KDTree,
pca=false, pca_dimension=false)
```

Aurora with `k`

-Nearest neighbors. If `looc=false`

, then `k`

is chosen equal to `kKNN`

, while if `loocv=true`

, then `k`

is selected for each held-out replicate by Leave-One-Out Cross-validation among the choices 1,...,`kKNN`

.

`tree`

describes the nearest neighbor computation strategy. The following options are available: `:auto`

, as well as , `:kdtree`

, `:balltree`

and `:brutetree`

from the `NearestNeighbors.jl`

package.

If `pca=true`

, a dimension reduction strategy is employed to find nearest neighbors using PCA (principal component analysis). For each held-out replicate, the order statistics are projected into the principal component subspace of dimension `pca_dimension`

. Note that in this case, the resulting nearest neighbors may only be interpreted as approximate nearest neighbors.

`Aurora.Auroral`

— Type`Auroral()`

Aurora with linear regression.

`Aurora.ReplicatedSample`

— Type`ReplicatedSample(Z::AbstractVector)`

This type represents `K`

iid samples $Z_{i1},\dotsc, Z_{iK}$ drawn from the same distribution $F_i$. In the setting, for which Aurora was developed, the distribution $F_i$`is parameterized by its mean`

`\mu_i`

`, i.e.,

\[\mu_i = \mathbb E_{F_i}[ Z_{ij}],\]

as well as a nuisance parameter $�lpha_i$, so that $F_i = F(\cdot \mid \mu_i, \alpha_i)$ and

\[Z_{i1},\dotsc, Z_{iK} \mid \mid \mu_i, \alpha_i \; \sim \; F(\cdot \mid \mu_i, \alpha_i).\]