During my PhD I will consider the problem of generalising statistics to data in a non-linear space. The interest for making statistical analyses on anatomical shapes have increased over time. The problem is that such data does not form a vector space. In fact we will assume the data to belong to a non-linear manifold. This means that it is not possible to apply the statistical theory which have been developed through time for euclidean data. Our goal is to make a contribution to the development of a consistent statistical theory for data on manifolds.