On nonlinear TAR processes and threshold estimation

P. Chigansky*, Yu A. Kutoyants

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We consider the problem of threshold estimation for autoregressive time series with a "space switching" in the situation when the regression is nonlinear and the innovations have a smooth, possibly non-Gaussian, probability density. Assuming that the unknown threshold parameter is sampled from a continuous positive prior density, we find the asymptotic distribution of the Bayes estimator. As is usual in the singular estimation problems, the sequence of Bayes estimators is asymptotically efficient, attaining the minimax risk lower bound.

Original languageAmerican English
Pages (from-to)142-152
Number of pages11
JournalMathematical Methods of Statistics
Issue number2
StatePublished - Apr 2012


  • Bayes estimator
  • compound Poisson process
  • likelihood inference
  • limit distribution
  • nonlinear threshold models
  • singular estimation


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