Non-Parametric Estimation Task
A Non-Parametric Estimation Task is an estimation task that does not require a parametric model.
- Context:
- It can be solved by a Non-Parametric Estimation System (that implements a non-parametric estimation algorithm).
- Example(s):
- Counter-Example(s):
- See: Non-Parametric Learning.
References
2012
- http://mathworld.wolfram.com/NonparametricEstimation.html
- QUOTE: Nonparametric estimation is a statistical method that allows the functional form of a fit to data to be obtained in the absence of any guidance or constraints from theory. As a result, the procedures of nonparametric estimation have no meaningful associated parameters. Two types of nonparametric techniques are artificial neural networks and kernel estimation.
Artificial neural networks model an unknown function by expressing it as a weighted sum of several sigmoids, usually chosen to be logit curves, each of which is a function of all the relevant explanatory variables. This amounts to an extremely flexible functional form for which estimation requires a nonlinear least-squares iterative search algorithm based on gradients.
Kernel estimation specifies y=m(x)+e, where m(x) is the conditional expectation of y with no parametric form whatsoever, and the density of the error e is completely unspecified. The N observations y_i and x_i are used to estimate a joint density function for y and x. The density at a point (y_0,x_0) is estimated by seeing what proportion of the N observations are "close to" (y_0,x_0). This procedure involves the use of a function called a kernel to assign weights to nearby observations.
- QUOTE: Nonparametric estimation is a statistical method that allows the functional form of a fit to data to be obtained in the absence of any guidance or constraints from theory. As a result, the procedures of nonparametric estimation have no meaningful associated parameters. Two types of nonparametric techniques are artificial neural networks and kernel estimation.