Background: The Data-Driven Identification method is a model-free approach to the identification of the mechanical stress in parts subject to statically indeterminate stress states. Although the method has been applied in many studies, no theoretical analysis of its convergence has been proposed so far. Purpose: The aim of this manuscript is to propose a first study of the DDI properties in order to increase the confidence in the results and guide the selection of optimal parameters. Methods: A new formulation w.r.t. the original one is proposed in order to expose an explicit minimization problem that is more prone to analysis. The algebraic characteristics of the new formulation are studied to derive properties of interest. Results: A simple criterion for the uniqueness of the DDI estimate is derived. In the case of elastic material behavior, an estimate of the error on the identified stress field is proposed. These results are illustrated on a synthetic data set. Conclusion: This work proposes a first analysis of the DDI and demonstrates the ability of the method to compute a model-free estimation of the stress field. The developed criteria and estimator open the door to further developments for the improvement of the method, the design of sample geometries loading path and extension to other classes of material behavior.