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On second order efficient robust inference |
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| Affiliation: | 1. Department of Statistics, University of Illinois at Urbana Champaign, 725 S. Wright Street, Champaign, IL 61820, USA;2. Bayesian and Interdisciplinary Research Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India;1. Department of Geographical Sciences, University of Maryland, College Park, MD 20740, United States;2. University of Tennessee, Knoxville, TN 37996, United States;3. Science Systems and Applications Inc., NASA Goddard Space Flight Center, Code 618, Greenbelt, MD 20771, United States;1. School of Electrical & Electronic Engineering, Universiti Sains Malaysia, Malaysia;2. School of Science and Technology, Wawasan Open University, Malaysia;3. Institute for Intelligent Systems Research and Innovation, Deakin University, Australia |
| Abstract: | 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. |
| Keywords: | Hellinger distance Minimum distance inference Negative exponential disparity Residual adjustment function Robustness Second order efficiency |
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