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时间序列统计量的渐近分布AI 解读

Verifiable conditions are given for the validity of formal Edgeworth expansions for the distribution of sums $X_1 + \cdots + X_n$, where $X_i = F(Z_i, \ldots, Z_{i + p - 1})$ and $Z_1, Z_2, \ldots$ is a strict sense stationary sequence that can be written as $Z_j = g(\varepsilon_{j - k}: k \geq 0)$ with an $\operatorname{iid}$ sequence $(\varepsilon_i)$ of innovations. These models include nonlinear functions of ARMA processes $(Z_i)$ as well as certain nonlinear AR…

后验分布的 Bernstein–von Mises 近似AI 解读

It is shown that under certain regularity conditions the Bernstein-v. Mises approximation of the posterior distributions is of order $O(n^{-\\frac{1}{2}})$ with high probability.