[R] How to translate the 2D-density matrix (the output of bkde2D function) into matrix of datapoints' amounts?

omega1x omega1x at gmail.com
Fri Sep 9 14:12:37 CEST 2011

It is known that function bkde2D (package "KernSmooth") returns a matrix of
density estimates over the mesh induced by x1 and x2. In Details it is
written that "... heights of the kernel, scaled by the bandwidths, at each
datapoint are summed. This sum, after a normalization, is the corresponding
fhat value in the output". 
There are several questions:
1) How to calculate amount (sum) of datapoints from this fhat value? Is it a
non-normalized matrix of fhat values?
2) Values in fhat matrix are greater than 1 sometimes, why? Values of
density are normalized and hence must be less than 1, isn't it?

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