Nonparametric Estimation
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 
, where 
is the conditional expectation of 
with no parametric form whatsoever, and the density of the error 
is completely unspecified. The 
observations 
and 
are used to estimate a joint density function for 
and 
. The density at a point 
is estimated by seeing what proportion of the 
observations are "close to" 
. This procedure involves the use of a function called a kernel to assign weights to nearby observations.
REFERENCES:
Kennedy, P. A Guide to Econometrics, 5th ed. Cambridge, MA: MIT Press, 1998.
Pagan, A. R. and Ullah, A. Non-Parametric Econometrics. Cambridge, England: Cambridge University Press, 1997.
Scott, D. W. Multivariate Density Estimation: Theory, Practice and Visualization. New York: Wiley, 1992.
