Aurora

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.

Auroral()

Aurora with linear regression.

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

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