Given a sample of a random variable supported by a smooth compact manifold
M⊂Rd, we propose a test to decide whether the boundary of
M is empty or not with no preliminary support estimation. The test statistic
is based on the maximal distance between a sample point and the average of its
kn-nearest neighbors. We prove that the level of the test can be estimated,
that, with probability one, its power is one for n large enough, and that
there exists a consistent decision rule. Heuristics for choosing a convenient
value for the kn parameter and identifying observations close to the
boundary are also given. We provide a simulation study of the test