Statistical inference based on a new weighted likelihood approach
We discuss a new weighted likelihood method for robust parametric estimation. The method is motivated by the need for generating a simple estimation strategy which provides a robust solution that is simultaneously fully efficient when the model is correctly specified. This is achieved by appropriate...
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| Vydáno v: | Metrika Ročník 84; číslo 1; s. 97 - 120 |
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01.01.2021
Springer Nature B.V |
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| ISSN: | 0026-1335, 1435-926X |
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| Abstract | We discuss a new weighted likelihood method for robust parametric estimation. The method is motivated by the need for generating a simple estimation strategy which provides a robust solution that is simultaneously fully efficient when the model is correctly specified. This is achieved by appropriately weighting the score function at each observation in the maximum likelihood score equation. The weight function determines the compatibility of each observation with the model in relation to the remaining observations and applies a downweighting only if it is necessary, rather than automatically downweighting a proportion of the observations all the time. This allows the estimators to retain full asymptotic efficiency at the model. We establish all the theoretical properties of the proposed estimators and substantiate the theory developed through simulation and real data examples. Our approach provides an alternative to the weighted likelihood method of Markatou et al. (J Stat Plan Inference 57(2):215–232, 1997; J Am Stat Assoc 93(442):740–750, 1998). |
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| AbstractList | We discuss a new weighted likelihood method for robust parametric estimation. The method is motivated by the need for generating a simple estimation strategy which provides a robust solution that is simultaneously fully efficient when the model is correctly specified. This is achieved by appropriately weighting the score function at each observation in the maximum likelihood score equation. The weight function determines the compatibility of each observation with the model in relation to the remaining observations and applies a downweighting only if it is necessary, rather than automatically downweighting a proportion of the observations all the time. This allows the estimators to retain full asymptotic efficiency at the model. We establish all the theoretical properties of the proposed estimators and substantiate the theory developed through simulation and real data examples. Our approach provides an alternative to the weighted likelihood method of Markatou et al. (J Stat Plan Inference 57(2):215–232, 1997; J Am Stat Assoc 93(442):740–750, 1998). |
| Author | Roy, Tania Bhandari, Subir Kumar Biswas, Adhidev Majumder, Suman Basu, Ayanendranath |
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| Cites_doi | 10.1007/BF02481146 10.1002/em.2860060207 10.1002/sta4.80 10.1214/aos/1176343997 10.1214/aoms/1177703732 10.1002/0471725382 10.1016/S0167-7152(01)00193-6 10.1016/S0167-7152(97)00136-3 10.2307/2527894 10.1093/biomet/85.3.549 10.1080/01621459.1998.10473726 10.1002/9780470316481 10.1080/02664760220136168 10.1080/00949650412331299120 10.1201/b10956 10.1214/aos/1021379866 10.2307/1403770 10.1111/j.0006-341X.2000.00483.x 10.1007/s00180-011-0301-1 10.1214/aos/1176325512 10.1016/S0378-3758(96)00045-6 10.1007/s11749-018-0596-0 10.1002/9781118165485 10.1016/j.csda.2006.11.002 10.1007/BF00773476 10.1111/j.2517-6161.1987.tb01702.x 10.1111/j.2517-6161.1984.tb01288.x |
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| Keywords | Influence function Robustness Robust regression Weighted likelihood Asymptotic efficiency |
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| Title | Statistical inference based on a new weighted likelihood approach |
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