In this work, we focus on Anomalous Change Detection (ACD), whose goal is the detection of small changes occurred between two hyperspectral images (HSI) of the same scene. When data are collected by airborne platforms, perfect registration between images is very difficult to achieve, and therefore a residual mis-registration (RMR) error should be taken into account in developing ACD techniques. Recently, the Local Co-Registration Adjustment (LCRA) approach has been proposed to deal with the performance reduction due to the RMR, providing excellent performance in ACD tasks. In this paper, we propose a method to estimate the first and second order statistics of the RMR. The RMR is modeled as a unimodal bivariate random variable whose mean value and covariance matrix have to be estimated from the data. In order to estimate the RMR statistics, a feature description of each image is provided in terms of interest points extending the Scale Invariant Feature Transform (SIFT) algorithm to hyperspectral images, and false matches between descriptors belonging to different features are filtered by means of a highly robust estimator of multivariate location, based on the Minimum Covariance Determinant (MCD) algorithm. In order to assess the performance of the method, an experimental analysis has been carried out on a real hyperspectral dataset with high spatial resolution. The results highlighted the effectiveness of the proposed approach, providing reliable and very accurate estimation of the RMR statistics.