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 |

`...` |
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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