  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.
