Stochastic Kernel

A stochastic kernel is the transition function of a (usually discrete) stochastic process. Often, it is assumed to be iid, thus a probability density function

Examples

  • The uniform kernel is 1/2 for -1.
  • The triangular kernel is 1-|t| for -1.
  • The quartic kernel is 15/26(1-t^2)^2 for -1.
  • The Epanechnikov kernel is 3/4(1-t^2) for -1.
Often, the data is fittet to such a kernel by setting a window width h, considering only x_i's in x \pm h/2 and setting t_i = (x_i-x)/h.

 

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