Weakly Adaptive Estimators in Explosive Autoregression
爆炸性自回归中的弱自适应估计量
Consider the model $X_i = \rho X_{i - 1} + \varepsilon_i, |\rho| > 1$, where $X_0, \varepsilon_1, \varepsilon_2, \cdots$ are independent random variables with $\varepsilon_1, \varepsilon_2, \cdots$ having common density $\psi$. This paper gives sufficient conditions under which the sequence of experiments induced by $\{X_0, X_1, \cdots, X_n\}$ has a weak limit in the sense of Le Cam. In general, the limiting experiment is translation invariant and neither LAN nor LAMN. The…