Effect of parameter estimation on fertilizer optimization

It is important to optimize the amount of fertilizer applied to a crop, both to improve profitability and to reduce environmental damage. Previous work has concentrated mainly on modelling the response of production to fertilizer. Here the authors complement this work by concentrating on the effect of parameter estimation on the value of the objective function. A simple expression for confidence intervals for the value of the true optimal strategy is obtained. Also, a risk function for the effect of using an estimated optimal strategy is proposed, and a simple estimator derived. The results are applied first to fertilizer optimization for a single field, and then for a population of fields.