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get bandwidth obtained from kde_lscv #68

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get bandwidth obtained from kde_lscv #68

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2 changes: 1 addition & 1 deletion src/KernelDensity.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -9,7 +9,7 @@ import StatsBase: RealVector, RealMatrix
import Distributions: twoπ, pdf
import FFTW: rfft, irfft

export kde, kde_lscv, UnivariateKDE, BivariateKDE, InterpKDE, pdf
export kde, kde_lscv, UnivariateKDE, BivariateKDE, InterpKDE, pdf, lscv_bw

abstract type AbstractKDE end

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40 changes: 40 additions & 0 deletions src/univariate.jl
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Expand Up @@ -162,6 +162,35 @@ end
# B. W. Silverman (1986)
# sections 3.4.3 (pp. 48-52) and 3.5 (pp. 61-66)

function lscv_bw(data::RealVector, midpoints::R;
kernel=Normal,
bandwidth_range::Tuple{Real,Real}=(h=default_bandwidth(data); (0.25*h,1.5*h)),
weights=default_weights(data)) where R<:AbstractRange

ndata = length(data)
k = tabulate(data, midpoints, weights)

# the ft here is K/ba*sqrt(2pi) * u(s), it is K times the Yl in Silverman's book
K = length(k.density)
ft = rfft(k.density)

ft2 = abs2.(ft)
c = -twoπ/(step(k.x)*K)
hlb, hub = bandwidth_range

opt = Optim.optimize(hlb, hub) do h
dist = kernel_dist(kernel, h)
ψ = 0.0
for j = 1:length(ft2)-1
ks = real(cf(dist, j*c))
ψ += ft2[j+1]*(ks-2.0)*ks
end
ψ*step(k.x)/K + pdf(dist,0.0)/ndata
end

return Optim.minimizer(opt)
end

function kde_lscv(data::RealVector, midpoints::R;
kernel=Normal,
bandwidth_range::Tuple{Real,Real}=(h=default_bandwidth(data); (0.25*h,1.5*h)),
Expand Down Expand Up @@ -213,3 +242,14 @@ function kde_lscv(data::RealVector;
midpoints = kde_range(boundary,npoints)
kde_lscv(data,midpoints; kernel=kernel, bandwidth_range=bandwidth_range, weights=weights)
end

function lscv_bw(data::RealVector;
boundary::Tuple{Real,Real}=kde_boundary(data,default_bandwidth(data)),
npoints::Int=2048,
kernel=Normal,
bandwidth_range::Tuple{Real,Real}=(h=default_bandwidth(data); (0.25*h,1.5*h)),
weights::Weights = default_weights(data))

midpoints = kde_range(boundary,npoints)
lscv_bw(data,midpoints; kernel=kernel, bandwidth_range=bandwidth_range, weights=weights)
end