Drowsy driving is pervasive, and also a major cause of traffic accidents. Estimating a driver's drowsiness level by monitoring the electroencephalogram (EEG) signal and taking preventative actions accordingly may improve driving safety. However, individual differences among different drivers make this task very challenging. A calibration session is usually required to collect some subject-specific data and tune the model parameters before applying it to a new subject, which is very inconvenient and not user-friendly. Many approaches have been proposed to reduce the calibration effort, but few can completely eliminate it. This paper proposes a novel approach, feature weighted episodic training (FWET), to completely eliminate the calibration requirement. It integrates two techniques: feature weighting to learn the importance of different features, and episodic training for domain generalization. Experiments on EEG-based driver drowsiness estimation demonstrated that both feature weighting and episodic training are effective, and their integration can further improve the generalization performance. FWET does not need any labelled or unlabelled calibration data from the new subject, and hence could be very useful in plugand-play brain-computer interfaces.