On second order efficient robust inference

General strategies for constructing second order efficient robust distances from suitable properties of the residual adjustment functions (RAF) are discussed. Based on those properties families of estimators are constructed using the truncated polynomial, negative exponential and sigmoidal functions as RAFs and their efficiency and robustness properties are investigated. The estimators have full asymptotic efficiency, and are automatically second order efficient. Many of the proposed estimators are competitive or better than the minimum Hellinger distance estimator (MHDE) and minimum negative exponential disparity estimator (MNEDE) under the combined goals of asymptotic efficiency with strong robustness properties. Hence the proposed families give the user the flexibility to choose from a large class of robust second order efficient estimators based upon specific needs.