  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 density, we find the asymptotic distribution of the Bayes
estimator. As usually in the singular estimation problems, the sequence of
Bayes estimators is found to be asymptotically efficient, attaining the minimax
risk lower bound.
