A central limit theorem for conditionally centred random fields with an application to testing statistical hypotheses

0411068 - UTIA-B 20030055 RIV HU eng C - Konferenční příspěvek (zahraniční konf.)
Janžura, Martin
A central limit theorem for conditionally centred random fields with an application to testing statistical hypotheses.
Budapest: János Bolyai Mathematical Society, 2002. In: Limit Theorems in Probability and Statistics. - (Berkes, I.; Csáki, E.; Csörgö, M.), s. 209-223
[Limit Theorems in Probability and Statistics. Balatonlelle (HU), 28.06.1999-02.07.1999]
Grant CEP: GA ČR GA201/99/0269
Výzkumný záměr: CEZ:AV0Z1075907
Klíčová slova: central limit theorem * conditionally centred random fields * composite hypotheses
Kód oboru RIV: BA - Obecná matematika

We prove a central limit theorem for conditionally centered random field, under condition of strict positivity of the empirical variance per observation. We use a random normalization, which fits to non-stationary situations. The theorem directly applied to Markov random fields, including the case of phase transition and lack of stationarity. A consequence is the asymptotic normality of a statistics for testing a composite hypotheses on a parameter of Markov fields in complete generality.
Trvalý link: http://hdl.handle.net/11104/0131155