# HigherOrderKernels.jl

**Repository Path**: Julialang/HigherOrderKernels.jl

## Basic Information

- **Project Name**: HigherOrderKernels.jl
- **Description**: No description available
- **Primary Language**: Unknown
- **License**: MIT
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2018-03-12
- **Last Updated**: 2024-10-11

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# 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.

![](kernels.svg)

# Example

```julia
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")
```

![](example.svg)

# 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