asycovTkTl: Asymptotic Covariance between T_k and T_l Values

In nnspat: Nearest Neighbor Methods for Spatial Patterns

Asymptotic Covariance between T_k and T_l Values

Description

This function computes the asymptotic covariance between T_k and T_l values which is used in the computation of the asymptotic variance of Cuzick and Edwards T_{comb} test, which is a linear combination of some T_k tests. The limit is as n_1 goes to infinity.

The argument, n_1, is the number of cases (denoted as n1 as an argument). The number of cases are denoted as n_1 and number of controls as n_0 in this function to match the case-control class labeling, which is just the reverse of the labeling in \insertCitecuzick:1990;textualnnspat.

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

Usage

asycovTkTl(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 asymptotic covariance between T_k and T_l values.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

covTkTl, 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)

asycovTkTl(Y,n1,k,l)
asycovTkTl(Y,n1,k,l,nonzero.mat = FALSE)
asycovTkTl(Y,n1,k,l,method="max")

nnspat documentation built on May 29, 2024, 10:03 a.m.