On Sep 9, 2011, at 8:12 AM, omega1x wrote:

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?

Wouldn't you just use 'cut' or 'findInterval' using the mesh points and then 'table' or 'tabulate'?

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?

No. One would expect that the normalization is done to get the integral equal to 1, not the individual points to have fhat in the range of [0,1]. (Failure to understand the difference is a common cause of questions on Rhelp, so if you need further explanation and many examples then do a search.)


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