Assume we have a problem of estimation of a density $f(x)$ over an interval $[0, 1]$. Can a regular histogram (i.e. with equal-sized bins) be viewed as some kind of a kernel?
3
-
1$\begingroup$ A histogram is applying a uniform kernel but what you see is an evaluation for the midpoints of each bin, extended to be shown as the same density estimate for all of the bin. Otherwise put, a kernel is applied disjointly on a grid of points. (As that is what happens in practice with some routines, the similarities are a little greater in practice than in principle.) It is largely convenience that histograms may show frequencies, proportions or percents rather than densities, but that's important: even some statistical people can get confused if they see densities above 1 (ignoring units). $\endgroup$– Nick CoxCommented Apr 13, 2021 at 8:18
-
1$\begingroup$ Something like this is often a good way in to explaining kernel density estimation, as (1) why a uniform kernel (2) why estimate discretely any way? $\endgroup$– Nick CoxCommented Apr 13, 2021 at 8:24
-
1$\begingroup$ For data on an interval, kernel density estimation is often awkward whenever your routine wants to smooth the distribution beyond the limits. There are fixes for that, but it's often ignored as secondary or just a nuisance. $\endgroup$– Nick CoxCommented Apr 13, 2021 at 8:27
Add a comment
|