Description Usage Arguments Details Value References See Also Examples

Calculate *\hat{η}_n* (the unconditional version of graph-based KPC) using directed K-NN graph or minimum spanning tree (MST).

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`Y` |
a matrix of response (n by dy) |

`X` |
a matrix of predictors (n by dx) |

`k` |
a function |

`Knn` |
the number of K-nearest neighbor to use; or "MST". |

*\hat{η}_n* is an estimate of the population kernel measure of association, based on data *(X_1,Y_1),… ,(X_n,Y_n)\sim μ*.
For K-NN graph, ties will be broken at random. MST is found using package `emstreeR`

.
In particular,

*\hat{η}_n:=\frac{n^{-1}∑_{i=1}^n d_i^{-1}∑_{j:(i,j)\in\mathcal{E}(G_n)} k(Y_i,Y_j)-(n(n-1))^{-1}∑_{i\neq j}k(Y_i,Y_j)}{n^{-1}∑_{i=1}^n k(Y_i,Y_i)-(n(n-1))^{-1}∑_{i\neq j}k(Y_i,Y_j)},*

where *G_n* denotes a MST or K-NN graph on *X_1,… , X_n*, *\mathcal{E}(G_n)* denotes the set of edges of *G_n* and
*(i,j)\in\mathcal{E}(G_n)* implies that there is an edge from *X_i* to *X_j* in *G_n*.
Euclidean distance is used for computing the K-NN graph and the MST.

The algorithm returns a real number ‘KMAc’, the empirical kernel measure of association

Deb, N., P. Ghosal, and B. Sen (2020), “Measuring association on topological spaces using kernels and geometric graphs” <arXiv:2010.01768>.

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