Component of the distance to build a stationary kernel function or similar.
$$M=\sum {w_i*(x'_i-x_i^{T})}^{power}$$
where $x_i$ is the $i^{th}$ column of the input matrix; $w_i$ is the $i^{th}$ element of the weight vector. Note that $x$ and $x'$ might be different.
Usage
xixj_sta(mat,mat.new=NULL,w=NULL,power=NULL)
Arguments
mat
Input data, could be a matrix or a vector.
mat.new
Second input data, could be a vector or a matrix. Default to be NULL. If NULL, mat.new=mat.
w
Weight to be add on each column of the matrix.
power
Argument 'power' X 2 will be the power to put on the distance. Default power is 1, which means $distance^2$. The range of the power to put on the distance is 0 to 2, thus argument 'power' is from 0 to 1.
Value
outA symmetric matrix used to build the linear kernel or similar
Details
If one wants to involve stationary kernel components in customized covariance matrix, this function will be used in derivatives of the kernel function. See examples in demo('co2').
References
Shi, J Q., and Choi, T. (2011), Gaussian Process Regression Analysis for Functional Data, Springer, New York.