# var.nnsym: Variances of Differences of Off-Diagonal Entries in an NNCT In nnspat: Nearest Neighbor Methods for Spatial Patterns

## Description

Returns the variances of differences of off-diagonal cell counts N_{ij}-N_{ji} for i,j=1,…,k and i \ne j in the NNCT, ct in a vector of length k(k-1)/2, the order of i,j for N_{ij}-N_{ji} is as in the output of ind.nnsym(k). These variances are valid under RL or conditional on Q and R under CSR.

## Usage

 1 var.nnsym(covN) 

## Arguments

 covN The k^2 \times k^2 covariance matrix of row-wise vectorized entries of NNCT

## Value

A vector of length k(k-1)/2, whose entries are the variances of differences of off-diagonal cell counts N_{ij}-N_{ji} for i,j=1,…,k and i \ne j in the NNCT.

Elvan Ceyhan

## References

\insertAllCited

var.nnct, var.tct and cov.nnct
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 n<-20 #or try sample(1:20,1) Y<-matrix(runif(3*n),ncol=3) ipd<-ipd.mat(Y) cls<-sample(1:2,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10)) ct<-nnct(ipd,cls) W<-Wmat(ipd) Qv<-Qvec(W)$q Rv<-Rval(W) varN<-var.nnct(ct,Qv,Rv) covN<-cov.nnct(ct,varN,Qv,Rv) #default is byrow var.nnsym(covN) ############# n<-40 Y<-matrix(runif(3*n),ncol=3) ipd<-ipd.mat(Y) cls<-sample(1:4,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10)) ct<-nnct(ipd,cls) W<-Wmat(ipd) Qv<-Qvec(W)$q Rv<-Rval(W) varN<-var.nnct(ct,Qv,Rv) covN<-cov.nnct(ct,varN,Qv,Rv) var.nnsym(covN)