论文标题
关于尖峰型变更点模型的错误指定
On misspecification in cusp-type change-point models
论文作者
论文摘要
I.I.D.参数估计的问题在错误指定的情况下，考虑了对不均匀泊松过程的观察。该模型是在存在同质泊松噪声的情况下观察到的泊松信号的模型。该过程的强度函数应该在变化点（信号到达的未知力矩）上具有尖型型奇异性，而信号的假定（理论）和真实（观察到的）水平则不同。描述了伪MLE的渐近特性。结果表明，估算器会收敛到最小化kullback-leibler差异的值，估计的归一化误差会收敛到一定极限分布，并且其多项式矩也会收敛。
The problem of parameter estimation by i.i.d. observations of an inhomogeneous Poisson process is considered in situation of misspecification. The model is that of a Poissonian signal observed in presence of a homogeneous Poissonian noise. The intensity function of the process is supposed to have a cusp-type singularity at the change-point (the unknown moment of arrival of the signal), while the supposed (theoretical) and the real (observed) levels of the signal are different. The asymptotic properties of pseudo MLE are described. It is shown that the estimator converges to the value minimizing the Kullback-Leibler divergence, that the normalized error of estimation converges to some limit distribution, and that its polynomial moments also converge.
