p.863

On the Estimation of an Exponential Function

M. T. G. Meulenberg

Abstract

In estimating a function, certain assumptions are made about the random term. This paper deals with the influence of such assumptions on estimators for the function $y = x^{\alpha}$. The case of a normally distributed random term, both in its multiplicative and additive forms, is considered here. The major part of the article is devoted to a hypothesis concerning a lognormally distributed random term, for which consistent estimators are derived.