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The 1972 Wald Lecture Robust Statistics: A Review

The 1972 Wald Lecture Robust Statistics: A Review,10.1214/aoms/1177692459,The Annals of Mathematical Statistics,Peter J. Huber

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The 1972 Wald Lecture Robust Statistics: A Review (Citations: 76)


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This is a selective review on robust statistics, centering on estimates of location, but extending into other estimation and testing problems. After some historical remarks, several possible concepts of robustness are critically reviewed. Three important classes of estimates are singled out and some basic heuristic tools for assessing properties of robust estimates (or test statistics) are discussed: influence curve, jackknifing. Then we give some asymptotic and finite sample minimax results for estimation and testing. The material is complemented by miscellaneous remarks on: computational aspects; other estimates; scale, regression, time series and other estimation problems; some tentative practical recommendations.

Journal: The Annals of Mathematical Statistics , vol. 43, no. 1972, pp. 1041-1067, 1972

DOI: 10.1214/aoms/1177692459

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Citation Context (4)

- ...Huber-loss [16, 17] for regression or loss functions for classification like maximum likelihood or the hinge loss used for support vector machines [16], then one obtains a nonlinear optimization problem, as in this section...
Gregory Beylkin, et al. Multivariate Regression and Machine Learning with Sums of Separable Fu...
- ...It is defined for statistics that can be written as functionals of the empirical distribution Pn as Vn = V (Pn) (either exactly or at least approximately), see Huber [6] for a review...
F. Chebana. Parametric estimation with a class of M -estimators
- ...circumstances. More details about this technique can be found in Huber (1972), Hoaglin et al. (1983) and Lee (1995) .I t is worth noting that the trimming procedure is applied here in a slightly different context...
Baudouin Desclée, et al. Forest change detection by statistical object-based method
- ...Huber 1964, 1972; Krarup et al. 1980) or combinations of them (see e.g...
- ...The previous section argues that the assumption that normality is equivalent to Hooke’s law was invented to make the energy quadratic (see also Huber 1972), probably in order to keep its minimization mathematically manageable...
J. Saleh. Robust estimation based on energy minimization principles

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Keywords (3)

The 1972 Wald Lecture Robust Statistics: A Review,10.1214/aoms/1177692459,The Annals of Mathematical Statistics,Peter J. Huber

Citation Context (4)

Gregory Beylkin, et al. Multivariate Regression and Machine Learning with Sums of Separable Fu...

F. Chebana. Parametric estimation with a class of M -estimators

Baudouin Desclée, et al. Forest change detection by statistical object-based method

J. Saleh. Robust estimation based on energy minimization principles

Citations (76)

The Empirical Likelihood method applied to covariance matrix estimation

Ensemble data assimilation with the CNMCA regional forecasting system

M split(q) estimation: estimation of parameters in a multi split functional model of geodetic observations

Multivariate Regression and Machine Learning with Sums of Separable Functions (Citations: 10)

Estimation of parameters in a split functional model of geodetic observations ( M split estimation) (Citations: 2)


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