Curve Fitting to Step Functions

Oscar R. Burt

American Journal of Agricultural Economics, 1964, vol. 46, issue 3, 662-672

Abstract: The methods presented in this paper provide an improved technique for fitting a continuous function to discontinuous step functions so often evolving from empirical studies such as estimation of demand and supply functions by linear programming. Curve fitting to step functions is analyzed using the criterion of minimizaton of the integral of squared distances between the curve being fitted and a step function. The criterion is a limiting form of least squares fit where all points on the step function are treated as "observations." Derivations are given for equations specifying the minimum integral fit for polynomials, a criterion of fit analogous to the coefficient of multiple determination in least squares fitting, and the analogue of the standard error of estimate in least squares.

Date: 1964
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