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.