Nt.def: N_t Value (found with the definition formula)

In elvanceyhan/nnspat: Nearest Neighbor Methods for Spatial Patterns

N_t Value (found with the definition formula)

Description

This function computes the N_t value which is required in the computation of the asymptotic variance of Cuzick and Edwards T_k test. Nt is defined on page 78 of (\insertCitecuzick:1990;textualnnspat) as follows. N_t= ∑ ∑_{i \ne l}∑ a_{ij} a_{lj} (i.e, number of triplets (i,j,l) i,j, and l distinct so that j is among kNNs of i and j is among kNNs of l).

This function yields the same result as the asyvarTk and varTk functions with $Nt inserted at the end.

See (\insertCitecuzick:1990;textualnnspat) for more details.

Usage

Nt.def(a)

Arguments

a	The A=(a_{ij}) matrix. The argument a is the A matrix, obtained as output fromm aij.mat.

Value

Returns the N_t value standing for the number of triplets (i,j,l) i,j, and l distinct so that j is among kNNs of i and j is among kNNs of l. See the description.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

asyvarTk, varTk, and varTkaij

Examples

n<-20  #or try sample(1:20,1)
Y<-matrix(runif(3*n),ncol=3)
k<-2 #try also 2,3
a<-aij.mat(Y,k)
Nt.def(a)

elvanceyhan/nnspat documentation built on Sept. 4, 2022, 10:28 a.m.