Some methods for using experimental data to estimate functions

Abstract

This paper serves three purposes 1) A general method is given by which one may correct for a bias that results when the maximum-likelihood method is used with a sample of finite size. The application to the problem of unfolding an unknown function from experimental data is discussed. 2) A method is given by which one may determine if the data require the existence of structure in an unknown function. This technique unfolds a function from data without parametrizing;i.e. without assuming that the function is a known function with unknown parameters. If, on the other hand, one is able to reliably parametrize an unknown function, but does not know the functional form of the background to the measurement, a method is supplied for making the foreground-background separation without parametrizing the background. 3) A method is given for improving the effective resolution of experimental measurements. This method is a generalization of «bremsstrahlung end-point subtraction», a common technique in high-energy photon physics.