The asymptotic decision theory by Le Cam and Hajek has been given a lucid perspective by the Ibragimov-Hasminskii theory on convergence of the likelihood random field. Their scheme has been applied to stochastic processes by Kutoyants, and today this plot is called the IHK program. This scheme ensures that asymptotic properties of an estimator follow directly from the convergence of the random field if a large deviation estimate exists. The quasi-likelihood analysis (QLA) proved a polynomial type large deviation (PLD) inequality to go through a bottleneck of the program. A conclusion of the QLA is that if the quasi-likelihood random field is asymptotically quadratic and if a key index reflecting identifiability the random field has is non-degenerate, then the PLD inequality is always valid, and as a result, the IHK program can run. Many studies already took advantage of the QLA theory. However, not a few of them are using it in an inefficient way yet. The aim of this paper is to provide a reformed and simplified version of the QLA and to improve accessibility to the theory. As an example of the effects of the theory based on the PLD, the user can obtain asymptotic properties of the quasi-Bayesian estimator by only verifying non-degeneracy of the key index.
翻译:Le Cam 和 Hajek 对概率随机字段趋同的Ibragimov-Hasminskii 理论对概率随机字段的趋同性决定理论给出了清晰的视角。 库托亚特人对随机场的随机过程应用了它们的图案, 今天这个图案被称为 IHK 程序。 这个方案确保随机场的偏差估计值的趋同性属性直接来自随机场的趋同性。 近似偏差分析( QLA) 证明它是一个多数值类型的大偏差( PLD), 要穿过程序的一个瓶颈。 QLA 的结论是, 如果准相似随机场的随机场被Kutoyantants应用于随机过程, 而今天这个图案称为 IHK 程序。 这个显示随机场可辨别性的关键指数是非异常的, 那么PLDA 只能运行 IHK 程序。 许多研究已经利用了QLA 理论。 然而, 只有少数研究在低效的路径上使用了它。 准的准LLA, 的精确的理论可以提供以简化和精确的理论。 A 的校正 。 的校正 。 的校正 。