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In this paper we present a new redescending M-estimator “Insha’s estimator†for robust regression and outliers detection that overcomes some drawbacks of other M-estimators for robust regression and outliers detection, such as destruction of the good observations and lack of simplicity in applications. The Ψ-function associated with the proposed estimator attains more linearity in the central section before it redescends, resulting in enhanced efficiency. Moreover the estimator is continuous everywhere and can be written in closed form without the use of an indictor function. The estimator is also applied to a real world example taken from the literature. For the purpose of comparison with other well-known redescending M-estimators extensive simulation study has been carried out. The example and simulation study show that using this estimator all the outliers can be successfully detected and is not affected by outliers.

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Ullah, I., Qadir, M. F., & Ali, A. (2006). Insha’s Redescending M-estimator for Robust Regression: A Comparative Study. Pakistan Journal of Statistics and Operation Research, 2(2), 135-144.