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

0411068 20240103182259.420060210235959.9 A central limit theorem for conditionally centred random fields with an application to testing statistical hypotheses Budapest János Bolyai Mathematical Society 2002 15 s. Limit Theorems in Probability and Statistics209-223BerkesI.CsákiE.CsörgöM. central limit theorem conditionally centred random fields composite hypotheses cav_un_auth*0101114 Janžura Martin UTIA-B Department of Stochastic Informatics Ústav teorie informace a automatizace AV ČR, v. v. i. 12A GA201/99/0269 GA ČR cav_un_auth*0005940 CEZ:AV0Z1075907 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. cav_un_auth*0213005 Limit Theorems in Probability and Statistics Balatonlelle HU 28.06.1999-02.07.1999 BA SI http://hdl.handle.net/11104/0131155 UTIA-B 20030055 2002 2002 Budapest János Bolyai Mathematical Society Limit Theorems in Probability and Statistics 209 223 Berkes I. 340 Csáki E. 340 Csörgö M. 340