Recent research on predictive video delivery promised optimal resource utilization and quality of service (QoS) satisfaction to both dynamic adaptive streaming over HTTP (DASH) providers and mobile users. These gains were attained while presuming an idealistic environment with perfect predictions. Thus, a robust QoS-aware predictive-DASH (P-DASH) is of paramount importance to handling the practical uncertainty implied in predicted information. In this paper, we propose a stochastic QoS-aware robust predictive-DASH (RP-DASH) scheme over future wireless networks that takes into account imperfect rate predictions. The objective is to achieve long-term quality fairness among the DASH users while capping the probability of service degradation by an operator predefined level. A deterministic formulation is then obtained using the scenario approximation, which adopts the probability density function (PDF) of predicted rates. A linear conservative approximation is introduced to provide an NP-complete formulation, which can be optimized by commercial solvers. Since exact PDF might not be available, Gaussian approximation is adopted by the introduced scheme to provide a closed form less complexity formulation. To support real-time implementations, a guided heuristic algorithm is devised to obtain near-optimal resource allocations and quality selections, while satisfying the predefined QoS level. Previous non-robust P-DASH schemes are evaluated in this paper, while considering typical error models in predicted rates. Such schemes resulted in increased QoS and the quality of experience degradations with the network load, which was avoided by the introduced RP-DASH. Results further revealed the ability of RP-DASH to reach optimal and fair QoS satisfactions.