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.

翻译：以 i.d.d. 观察不相容的 Poisson 过程的参数估计问题在误差的情况下被考虑。 模型是在同质Poissonian 噪音面前观测到的Poissonian 信号。 过程的强度功能在变化点( 信号到达的未知时刻) 上应该有一个微秒型的奇数, 而信号的假定( 理论) 和真实( 观察的) 水平是不同的。 描述的是伪 MLE 的无症状特性。 显示测算符与最小化 Kullback- Leibel 差异值的值相趋同, 估计的常态误差会聚集到某些限制分布, 其多位时也趋于一致 。