Bootstrapping Not Independent and Not Identically Distributed Data

Classical normal asymptotics could bring serious pitfalls in statistical inference, because some parameters appearing in the limit distributions are unknown and, moreover, complicated to estimated (from a theoretical as well as computational point of view). Due to this, plenty of stochastic approaches for constructing confidence intervals and testing hypotheses cannot be directly applied. Bootstrap seems to be a plausible alternative. A methodological framework for bootstrapping not independent and not identically distributed data is presented together with theoretical justification of the proposed procedures. Among others, bootstrap laws of large numbers and central limit theorems are provided. The developed methods are utilized in insurance and psychometry.

Automated summary

Classical normal asymptotics can pose challenges in statistical inference due to unknown and difficult-to-estimate parameters in the limit distributions. Bootstrap methods offer a plausible alternative and a methodological framework for non-independent and non-identically distributed data is presented, along with theoretical justification. These methods have been applied in insurance and psychometry.