covTkTl {nnspat}R Documentation

Finite Sample Covariance between TkT_k and TlT_l Values

Description

This function computes the exact (i.e., finite sample) covariance between TkT_k and TlT_l values which is used in the computation of the exact variance of Cuzick and Edwards TcombT_{comb} test, which is a linear combination of some TkT_k tests.

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

See page 80 of (Cuzick and Edwards (1990)) for more details.

Usage

covTkTl(dat, n1, k, l, nonzero.mat = TRUE, ...)

Arguments

dat

The data set in one or higher dimensions, each row corresponds to a data point.

n1

Number of cases

k, l

Integers specifying the number of NNs (of subjects ii and mm in aij(k)amj(l)a_{ij}(k) a_{mj}(l)).

nonzero.mat

A logical argument (default is TRUE) to determine whether the AA matrix or the matrix of nonzero locations of the AA matrix will be used in the computation of NsN_s and NtN_t. If TRUE the nonzero location matrix is used, otherwise the AA matrix itself is used.

...

are for further arguments, such as method and p, passed to the dist function.

Value

Returns the exact covariance between TkT_k and TlT_l values.

Author(s)

Elvan Ceyhan

References

Cuzick J, Edwards R (1990). “Spatial clustering for inhomogeneous populations (with discussion).” Journal of the Royal Statistical Society, Series B, 52, 73-104.

See Also

asycovTkTl, covTcomb, and Ntkl

Examples

n<-20  #or try sample(1:20,1)
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(0:1,n,replace = TRUE)  #or try cls<-rep(0:1,c(10,10))
n1<-sum(cls==1)

k<-1 #try also 2,3 or sample(1:5,1)
l<-1 #try also 2,3 or sample(1:5,1)
c(k,l)

covTkTl(Y,n1,k,l)
covTkTl(Y,n1,k,l,method="max")
asycovTkTl(Y,n1,k,l)

covTkTl(Y,n1,k,l,nonzero.mat = FALSE)
asycovTkTl(Y,n1,k,l,nonzero.mat = FALSE)


[Package nnspat version 0.1.2 Index]