Large Deviations of Estimators
估计量的大偏差
The performance of a sequence of estimators $\{T_n\}$ of $g(\theta)$ can be measured by its inaccuracy rate $-\lim \inf_{n\rightarrow\infty} n^{-1} \log \mathbb{P}_\theta(\|T_n - g(\theta)\| > \varepsilon)$. For fixed $\varepsilon > 0$ optimality of consistent estimators $\operatorname{wrt}$ the inaccuracy rate is investigated. It is shown that for exponential families in standard representation with a convex parameter space the maximum likelihood estimator is optimal. If…