I was reading about non-parametric kernel density estimation. http://en.wikipedia.org/wiki/Kernel_density_estimation
For uni-variate where D = 1, we can write like
For Multivariate Kernel density estimation (KDE), more preciously for d=3 and X = (x,y,z) can we write:
Is this technically correct? Can any one help with this?
This is very difficult to do on your own, and you really should do this through some package. Nevertheless, the definition is:
fH(x)= 1 / n \sum{i=1}n KH (x - xi), where
x = (x1, x2, …, xd)T, xi = (xi1, xi2, …, xid)T, i = 1, 2, …, n are d-vectors;
H is the bandwidth (or smoothing) d×d matrix which is symmetric and positive definite;
K is the kernel function which is a symmetric multivariate density;
KH(x) = |H|−1/n K(H−1/2x).