Ntkl: N_{tkl} Value In nnspat: Nearest Neighbor Methods for Spatial Patterns

Description

This function computes the N_{tkl} value which is required in the computation of the exact and asymptotic variance of Cuzick and Edwards T_{comb} test, which is a linear combination of some T_k tests. N_{tkl} is defined on page 80 of (\insertCitecuzick:1990;textualnnspat) as follows. Let a_{ij}(k) be 1 if j is a k NN of i and zero otherwise and N_t(k,l) = ∑ ∑_{i \ne m}∑ a_{ij}(k) a_{mj}(l).

The logical argument nonzero.mat (default=TRUE) is for using the A matrix if FALSE or just the matrix of nonzero locations in the A matrix (if TRUE) in the computations.

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

Usage

 1 Ntkl(dat, k, l, nonzero.mat = TRUE, ...)

Arguments

 dat The data set in one or higher dimensions, each row corresponds to a data point. k, l Integers specifying the number of NNs (of subjects i and m in a_{ij}(k) a_{mj}(l)). nonzero.mat A logical argument (default is TRUE) to determine whether the A matrix or the matrix of nonzero locations of the A matrix will be used in the computation of N_s and N_t (argument is passed on to asycovTkTl and covTkTl). If TRUE the nonzero location matrix is used, otherwise the A matrix itself is used. ... are for further arguments, such as method and p, passed to the dist function.

Value

Returns the N_{tkl} value. See the description.

Elvan Ceyhan

\insertAllCited