Cross-lingual transfer is a leading technique for parsing low-resource languages in the absence of explicit supervision. Simple `direct transfer' of a learned model based on a multilingual input encoding has provided a strong benchmark. This paper presents a method for unsupervised cross-lingual transfer that improves over direct transfer systems by using their output as implicit supervision as part of self-training on unlabelled text in the target language. The method assumes minimal resources and provides maximal flexibility by (a) accepting any pre-trained arc-factored dependency parser; (b) assuming no access to source language data; (c) supporting both projective and non-projective parsing; and (d) supporting multi-source transfer. With English as the source language, we show significant improvements over state-of-the-art transfer models on both distant and nearby languages, despite our conceptually simpler approach. We provide analyses of the choice of source languages for multi-source transfer, and the advantage of non-projective parsing. Our code is available online.
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