Influential point diagnosis for high-dimensional linear models

Advances in the field of influential point diagnosis are reviewed from both single and multiple influential point perspectives．Several new methods for high-dimensional influential point diagnosis developed in recent years are highlighted．The method is applicable to cases where the number of independent variables far exceeds sample size, and can be regarded as generalization of the classical Cook distance to high-dimensional data．The Cook distance measures effect of observations on least square coefficient estimates．In contrast, the new methods capture the effect of observations on marginal correlation, with important implications for variable selection and other downstream tasks．Numerical simulation results demonstrate effectiveness of these new methods．