covTkTl {nnspat}

Finite Sample Covariance between $T_k$ and $T_l$ Values

Description

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

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 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 $i$ 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 $N_t$. 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 exact covariance between $T_k$ and $T_l$ 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)