Object oriented inference methods

Resumo

Object oriented data analysis (OODA) can be defined as the statistical analysis of complex objects. This term comprises any situation where classical inferential techniques are not directly applicable, either because the population of study is supported on a manifold different from the Euclidean space, or because its characteristic of interest has an overly complex structure that usual statistic techniques cannot manage. This doctoral thesis addresses three problems included in the OODA framework: assessing the number of modes of a circular variable, estimating high density regions for data on manifolds, and developing locally optimal inference techniques for noisy directional data.