We investigate the performance of the ordinary least squares (OLS)-, M-, MM-, and the Theil–Sen (TS)-estimator for crop yield data analysis in crop insurance applications using Monte Carlo simulations. More specifically, the performance is assessed with respect to trend estimation, prediction of future yield levels, and the estimation of expected indemnity payments. In agreement with earlier findings, other estimators are found to be superior to OLS in simple regression problems if yield distributions are outlier contaminated and heteroscedastic. While this conclusion is also valid for subsequent applications such as yield prediction and the estimation of expected indemnity payments, the difference between the considered estimators becomes less distinct. For these applications, we find particularly the M-estimator to be a good compromise between high-breakdown (very robust) estimators and the very efficient OLS-estimator. Because no regression technique dominates all others in all applications and scenarios for error term distributions, our results underline that the choice of the estimation technique should be dependent on the purpose of the crop yield data analysis. However, alternative estimators such as M-, MM-, and TS-estimator can reduce (and bound) the risk of unreliable or inefficient crop yield data analysis in crop insurance applications.