M. Malyutov

SCOT Approximation and Asymptotic Inference I

Approximation of stationary strongly mixing processes by SCOT models and the Le Cam−Hajek−Ibragimov−Khasminsky locally minimax theory of statistical inference for them is outlined. SCOT is an m-Markov model with sparse memory structure. In our previous IP papers we proved SCOT equivalence to 1-Markov Chain with state space − alphabet consisting of the SCOT contexts. For the fixed alphabet size and growing sample size, the Local Asymptotic Normality is proved and applied for establishing asymptotically optimal inference. We outline what obstacles arise for a large SCOT alphabet size and not necessarily vast sample size.

КЛЮЧЕВЫЕ СЛОВА: strong mixing, strongly stationary sequences, Local Asymptotic Normality, Local Asymptotic Minimaxity, SCOT models, Edgeworth expansion