Data-informed influence analysis

The likelihood-based influence analysis methodology introduced in Cook (1986) uses a parameterised space of local perturbations of a base model. It is frequently the case that such perturbation schemes involve more parameters of interest and perturbation parameters than there are observations, and hence the perturbation space is often explored rather than estimated, where exploration means discovering the effect on inference of putatively choosing values of perturbation parameters. This paper considers the question of what can be learned about the perturbation parameters through the data. It extends Cook's methodology to take account of information available in the data regarding the perturbations, the general philosophy of the approach being that of learn what you can and explore what you cannot learn. Both local and global analyses are possible, as indicated by the data, while the eigenvector sign indeterminacy of local analysis is removed. Numerical examples are given and further developments are briefly indicated.