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8: Nonparametric, Derived, and Formula Distributions
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Core Algorithms
Create Confidence Envelopes about Nonparametric Density Estimates
Use several bandwidth-selection methods to determine a proper bandwidth. Estimate a bootstrapped 95% pointwise confidence band for the kernel density estimate.
In[1]:=
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data = BlockRandom[SeedRandom[3]; RandomVariate[ dist = MixtureDistribution[{1/2, 3, 1}, {NormalDistribution[-4, .4], NormalDistribution[0, 2], NormalDistribution[2.5, .6]}], 500]];
In[2]:=
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\[ScriptCapitalD] = SmoothKernelDistribution[data]; bSamp = RandomChoice[data, {250, Length[data]}]; Subscript[\[ScriptCapitalD], B] = SmoothKernelDistribution[#] & /@ bSamp;
In[3]:=
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pdf = Table[ PDF[i, rng = Range[-7., 7, .05]], {i, Subscript[\[ScriptCapitalD], B]}]; High = Table[Quantile[i, .975], {i, Transpose[pdf]}]; Low = Table[Quantile[i, .025], {i, Transpose[pdf]}]; p1 = Show[ ListLinePlot[{Transpose[{rng, High}], Transpose[{rng, Low}]}, Filling -> {1 -> {{2}, Automatic}}, PlotRange -> {0, .25}, PlotStyle -> Dashed], Plot[PDF[\[ScriptCapitalD], x], {x, -7, 7}, PlotStyle -> {Thick, Blue}, PlotRange -> {0, .25}], Frame -> True, Axes -> None, ImageSize -> 570]; dists2 = Table[ SmoothKernelDistribution[data, i], {i, {"Oversmooth", "Silverman", "SheatherJones"}}]; p2 = Plot[Evaluate[PDF[#, x] & /@ dists2], {x, -8, 8}, Frame -> True, Axes -> None, ImageSize -> 570]; Grid[{{p2}, {p1}}]
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