标题： 关于分数布朗运动的表示及其在尖点统计模型中出现的统计量的极限分布 显示英文标题

标题： On a representation of fractional Brownian motion and the limit distributions of statistics arising in cusp statistical models

摘要： 我们讨论了Chernoyarov等人近期论文（《统计数学年鉴》，2016年10月）中关于“信号加白噪声”模型下贝叶斯估计量和最大似然估计量极限分布结果的一些扩展。该模型中的信号具有不规则的尖峰类型。利用分数布朗运动(fBm)用尖峰函数表示的新方法，我们证明当噪声强度趋于零时，极限分布可以用fBm来表达，适用于所有不对称尖峰类型信号，相应地与赫斯特参数H有关，0<H<1。还提供了贝叶斯估计量和最大似然估计量极限分布密度和方差的模拟结果。 显示英文摘要

摘要： We discuss some extensions of results from the recent paper by Chernoyarov et al. (Ann. Inst. Stat. Math., October 2016) concerning limit distributions of Bayesian and maximum likelihood estimators in the model "signal plus white noise" with irregular cusp-type signals. Using a new representation of fractional Brownian motion (fBm) in terms of cusp functions we show that as the noise intensity tends to zero, the limit distributions are expressed in terms of fBm for the full range of asymmetric cusp-type signals correspondingly with the Hurst parameter H, 0<H<1. Simulation results for the densities and variances of the limit distributions of Bayesian and maximum likelihood estimators are also provided.