TY - JOUR
T1 - On nonlinear TAR processes and threshold estimation
AU - Chigansky, P.
AU - Kutoyants, Yu A.
PY - 2012/4
Y1 - 2012/4
N2 - 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.
AB - 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.
KW - Bayes estimator
KW - compound Poisson process
KW - likelihood inference
KW - limit distribution
KW - nonlinear threshold models
KW - singular estimation
UR - http://www.scopus.com/inward/record.url?scp=84864684572&partnerID=8YFLogxK
U2 - 10.3103/S1066530712020056
DO - 10.3103/S1066530712020056
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AN - SCOPUS:84864684572
SN - 1066-5307
VL - 21
SP - 142
EP - 152
JO - Mathematical Methods of Statistics
JF - Mathematical Methods of Statistics
IS - 2
ER -