funsAijmat | R Documentation |
Two functions: aij.mat
and aij.nonzero
.
The function aij.mat
yields the A=(a_{ij}(k)) matrix where a_{ij}(k) = 1 if z_j is among the k
NNs of z_i
and 0 otherwise due to \insertCitetango:2007;textualnnspat.
This matrix is useful in calculation of the moments of Cuzick-Edwards T_k tests.
The function aij.nonzero
keeps only nonzero entries, i.e., row and column entries where
in each row, for the entry (r_1,c_1) r_1 is the row entry and c_1 is the column entry. Rows are from
1 to n, which stands for the data point or observation, and column entries are from 1 to k
, where k
is specifying
the number of k
NNs (of each observation) considered. This function saves in storage memory, but needs to be
carefully unfolded in the functions to represent the actual the A matrix.
See also (\insertCitetango:2007;textualnnspat).
aij.mat(dat, k, ...) aij.nonzero(dat, k, ...)
dat |
The data set in one or higher dimensions, each row corresponds to a data point. |
k |
Integer specifying the number of NNs (of subject i), default is |
... |
are for further arguments, such as |
The function aij.mat
returns the A_{ij} matrix for computation of moments of Cuzick and Edwards T_k
Test statistic while the function aij.nonzero
returns the (locations of the) non-zero entries in the A_{ij}
matrix
Elvan Ceyhan
aij.theta
and EV.Tkaij
n<-20 #or try sample(1:20,1) Y<-matrix(runif(3*n),ncol=3) k<-3 #try also 2,3 Aij<-aij.mat(Y,k) Aij Aij2<-aij.mat(Y,k,method="max") range(Aij,Aij2) apply(Aij,2,sum) #row sums of Aij aij.nonzero(Y,k) aij.nonzero(Y,k,method="max")
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