Comparative Analysis of Cubic Spline and Kernel Estimation of a Probit Function

Author: Tahsoh J.T.

Source: Journal of Computational Analysis and Applications, Volume 3, Number 1, January 2001 , pp. 83-94(12)

Publisher: Springer

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Abstract:

The least-squares cubic spline and the kernel estimators produce comparable mean squared errors, although the kernel produces smaller mean squared errors when the variable increases away from 0. Mean squared error increases with an increase in the number of knots (for the cubic spline) or reduced band width (for the kernel estimator). The cubic spline produces smaller mean squared errors when all observations are made at knots than when they are spaced out between knots. Irrespective of the exact form of the probit function g(x), the cubic spline estimator is asymptotically unbiased, while the kernel estimator only converges to g(x) under certain conditions. Moreover, the cubic spline is a smooth function, which is twice differentiable on the interval [0,1].

Keywords: Least squares; cubic spline; mean squared error; kernel; probit function, expectation

Language: English

Document Type: Regular paper

Affiliations: 1: Department of Economics and Management, Faculty of Social and Management Sciences, University of Buea, Cameroon, West Africa.

Publication date: 2001-01-01