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I have implemented the KDE distribution finding for a dataset. I apply the adaptive bandwidth method; I want to plot the change in bandwidth over the entire distribution. How can I do it? Thank you! enter image description here

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The following will give you the adaptive bandwidths that Mathematica uses:

SeedRandom[12345];
data = RandomVariate[NormalDistribution[0, 1], 10] // Sort;

α = 0.6;
kmd = KernelMixtureDistribution[data, {"Adaptive", Automatic, α}];
bw = kmd[[2, 4]]
(* {0.455945, 0.367787, 0.354622, 0.350731, 0.340984, 0.33284, 0.335444, 0.336422,
    0.343412, 0.517947}{0.455945, 0.367787, 0.354622, 0.350731, 0.340984, 0.33284,
    0.335444, 0.336422, 0.343412, 0.517947} *)

However, these bandwidths do not match what R gives (using akj in the quantreg package) which is the same as I get doing this in Mathematica with a brute force method. I'll look at that more to see if I can figure out the difference.

One can then plot those adaptive bandwidths against the data values:

ListPlot[Transpose[{data, bw}], Frame -> True,
  FrameLabel -> {"Data value", "Adaptive bandwidth"}]

Data values vs adaptive bandwidth

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  • $\begingroup$ Can also use kmd["Weights"] to get the list kmd[[2, 4]] (+1) $\endgroup$
    – kglr
    Commented Feb 8 at 0:15
  • $\begingroup$ @kglr kmd["Weights"] seems to get kmd[[2,1]]. And maybe those weights might help explain the difference I get using R. $\endgroup$
    – JimB
    Commented Feb 8 at 0:24
  • $\begingroup$ sorry, I meant kmd["Bandwidth"]. $\endgroup$
    – kglr
    Commented Feb 8 at 0:30
  • $\begingroup$ Thank you so much. I solved it $\endgroup$
    – Tin Trung Chau
    Commented Mar 19 at 17:58

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