README.md

HigherOrderKernels

This package provides basic kernel density estimation using higher order kernels also known as bias reducing kernels. At the moment only kernels from the polynomial family described in [1] and the Gaussian family described in [2]. This includes some widely used kernels:

• Uniform
• Epanechnikov
• Biweight
• Triweight
• Gaussian

and higher order versions. Kernel code is generated automatically, so any order is possible.

For bandwidht selection, Silverman's rule-of-thumb is implemented for all kernels.

Example

using HigherOrderKernels
using Plots
using Distributions

data = randn(10000)
xgrid = linspace(-2, 2, 100)
plt = plot()
for ν = 2:2:8
  k = EpanechnikovKernel{ν}
  h = bandwidth(k, data)
  p = kpdf.(k, xgrid, [data], h)
  plot!(plt, xgrid, p, label="Order $ν")
end
plot!(x -> pdf(Normal(), x), label="Exact")

References

1. Hansen, B. E. (2005). EXACT MEAN INTEGRATED SQUARED ERROR OF HIGHER ORDER KERNEL ESTIMATORS. Econometric Theory, 21(6), 1031–1057. http://doi.org/10.1017/S0266466605050528
2. Wand, M. P., & Schucany, W. R. (1990). Gaussian-based kernels. The Canadian Journal of Statistics. La Revue Canadienne De Statistique, 18(3), 197–204. http://doi.org/10.2307/3315450?refreqid=search-gateway:c3a7da0239447971afa03cb0995530fd