Abstract
The paper traces the history of estimation of unknown parameters when measurements are subject to error from the time of Ptolemy to Gauss and Laplace, the inventors of the method of least squares estimation (LSE). The modern theory of LSE started with the papers by Markoff and Aitken and later contributions by Bose and the author. The LSE’s have some nice properties. However, they are found to be sensitive to outliers and contamination in the data. To overcome this defect, robust methods are introduced using measures of discrepancy between a measurement and its expected value which have a slower rate of growth than the squared value. A unified theory of robust estimation is described using the difference of two convex functions as the measure of discrepancy.
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Rao, C.R. (1997). Pre and Post Least Squares: The Emergence of Robust Estimation. In: Babu, G.J., Feigelson, E.D. (eds) Statistical Challenges in Modern Astronomy II. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1968-2_1
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DOI: https://doi.org/10.1007/978-1-4612-1968-2_1
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