Estimation for a One-Parameter Exponential Model

An estimation procedure, called the "partial totals" method, is presented, illustrated and evaluated for the model y = exp(-pt)+e when the values of t are equally spaced. Tables of estimates using this estimation procedure are given for the case where the smallest value of t is zero. The evaluation consists of an analytical investigation of the large sample properties of the partial totals estimator and a report on a comparative study of its small sample properties relative to three other estimators based on Monte Carlo results where it is assumed either that y is a binomial proportion or that y is a proportion with variance proportional to a binomial variance. It is shown that the partial totals estimator is asymptotically normal and consistent (but it is not asymptotically efficient). On the basis of the Monte Carlo study, the partial totals estimator is compared with the maximum likelihood, least squares (on the logarithms) and weighted least squares (on the logarithms) estimators. The comparison, based on relative efficiency indicates that the maximum liklihood and partial totals methods give similar results and were the most satisfactory over the range of conditions studied.