Robust Estimation of a Location Parameter
TLDR
In this article, a new approach toward a theory of robust estimation is presented, which treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators that are asyptotically most robust (in a sense to be specified) among all translation invariant estimators.Abstract:
This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators—intermediaries between sample mean and sample median—that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. For the general background, see Tukey (1960) (p. 448 ff.)read more
Citations
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The behavior of maximum likelihood estimates under nonstandard conditions
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References
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Probability theory
TL;DR: These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law of large numbers.
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A Class of Statistics with Asymptotically Normal Distribution
TL;DR: In this article, the authors considered the problem of estimating a U-statistic of the population characteristic of a regular functional function, where the sum ∑″ is extended over all permutations (α 1, α m ) of different integers, 1 α≤ (αi≤ n, n).
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Estimates of Location Based on Rank Tests
J. L. Hodges,Erich L. Lehmann +1 more
TL;DR: Rank tests such as the two Wilcoxon tests or the Kruskal-Wallis H-test have been shown to be more robust against gross errors than that of the t-and F-tests, even in the rare case in which the suspicion of the possibility of gross errors is unfounded.