Kernel Functions

A kernel function defines the smoothing behavior of the ASH estimator.

AverageShiftedHistograms can use any function as a kernel that satisifies the following properties:

  • Non-negative: f(x) >= 0
  • Symmetric: f(x) = f(-x)
Note

In most applications, kernels need to integrate to 1, but that is not required in AverageShiftedHistograms

Function in AverageShiftedHistograms.Kernels

The Kernels module defines a collection of kernels:

  • biweight (default)
  • cosine
  • epanechnikov
  • triangular
  • tricube
  • triweight
  • uniform
  • gaussian
  • logistic

See https://en.wikipedia.org/wiki/Kernel(statistics)#Kernelfunctionsincommon_use for detailed descriptions.