Different possible sources of data have been identified for computing yield gaps in the past, but statistical methods for yield gap estimation have received little attention. In this paper, we present a statistical model, called quantile regression, for estimating potential yields and yield gaps. The principle of our method is to estimate potential yields from high yield quantiles calculated using observed yield data. The originality of our approach is that it does not rely on climatic zones and data bins; crop yields are directly related to climatic variables using a regression quantile model. This method was applied in a case study on wheat production at the world scale. A model was defined to relate wheat yields to two climatic variables (soil moisture and temperature sum). The model parameters were estimated from a global wheat dataset, and the fitted model was used for calculating potential wheat yields and yield gaps in the world.Parameter estimates and their confidence intervals were presented for a series of quantiles ranging from the 90^th to the 99.9^th percentiles. Results showed that it was possible to estimate extreme quantiles (i.e., up to the 99.95^th percentile) with good level of accuracy in our case study. I will present the method and the case study, and I will show how the proposed statistical method can be implemented to compute yield gaps using the statistical R software.