Abstract

Through perturbing the Kullback-Leibler divergence, we demonstrate how to systematically robustify statistical inference for stochastic process models based on the conventional Gaussian quasi-likelihood (GQLF). We theoretically show that the modified GQLFs are robust against several finite-activity contaminations, such as jumps and spike noises. The estimation procedures involve one user-input tuning parameter lying in a bounded domain. Some illustrative simulation results are given, particularly showing the sensitivity of the estimation performance for fine-tuning. The proposed method is simple to use hence practical, and efficiently works even when there are no contaminations. The proposed strategy can be applied in analogous ways to other types of random dynamical systems such as diffusions with small noise contaminated by jumps and so on.