covTcomb {nnspat}

Covariance matrix for T_k values in Tcomb

Description

This function computes the covariance matrix for the T_k values used in the T_{comb} test statistics, which is a linear combination of some T_k tests.

The argument, n_1, is the number of cases (denoted as n1 as an argument). The number of cases is denoted as n_1 to match the case-control class labeling, which is just the reverse of the labeling in Cuzick and Edwards (1990).

The argument klist is the vector of integers specifying the indices of the T_k values used in obtaining the T_{comb}.

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.

The logical argument asy.cov (default=FALSE) is for using the asymptotic covariance or the exact (i.e., finite sample) covariance for the vector of T_k values used in Tcomb. If asy.cov=TRUE, the asymptotic covariance is used, otherwise the exact covariance is used.

See page 87 of (Cuzick and Edwards (1990)) for more details.

Usage

covTcomb(dat, n1, klist, nonzero.mat = TRUE, asy.cov = FALSE, ...)

Arguments

dat

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

n1

Number of cases

klist

list of integers specifying the indices of the T_k values used in obtaining the T_{comb}.

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.

asy.cov

A logical argument (default is FALSE) to determine whether asymptotic or exact (i.e., finite sample) covariances between T_k and T_l values are to be used to obtain the entries of the covariance matrix. If TRUE the asymptotic covariance values are used, otherwise exact covariance values are used.

...

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

Value

Returns the covariance matrix for the T_k values used in Tcomb.

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)

kl<-sample(1:5,3) #try also sample(1:5,2)
kl
covTcomb(Y,n1,kl)
covTcomb(Y,n1,kl,method="max")
covTcomb(Y,n1,kl,nonzero.mat = FALSE)

covTcomb(Y,n1,kl,asy=TRUE)