The Role of Robust Statistics in Private Data Analysis
Robust statistics can be described as a subfield of mathematical statistics that seeks to account for the fact that statistical models are, at best, only good approximations of reality. It became an active research area after Peter Huber’s breakthrough paper, “Robust estimation of a location parameter” (1964), which set the foundations for a promising new theory of statistics that rigorously defined the problem of robustness in the sense of insensitivity to small deviations from the assumptions and outliers. Paraphrasing Stephen Stigler, until that point, the question of robustness had only been poorly articulated as some trade-offs that applied statisticians had to make in practice.
Despite the excitement generated by robust statistics in the 1970s–80s, it is clear that it did not become the dominating view of statistics, even though the widely accepted idea that robustness is indeed a desired property for any statistical procedure (Stigler. 2010).
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