| R. Hampel, E.M. Ronchetti, P.J. Rousseeuw and W.A. Stahel, Robust Statistics. The approach Based on InfluenceFunction, Wiley & Sons --- New York, 1986. |
....M test since the least squares estimator is highly non robust to outliers. Therefore instead of using least squares estimation the regression parameter are estimated by a regression M estimator which uses Tukey s biweight function. For details about robust regression estimates see for example [6]. Again the tests are analysed 12 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 d rejection probability Figure 3: Power of the M (solid) and ML test (dashed) with standard normal distributed residuals after doing a linear regression in two situations. First u 2t is assumed to be ....
F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw, and W.A. Stahel. Robust Statistics. The Approach based on Influence Functions. Wiley, New York, 1986.
....(x 1 ; x k ) where L(x 1 ; x k ) P k . I write Pf for R fdP . 1[ x; y) 2 B] denotes the indicator function of the set B. 2 Clusters, outliers, M estimators and fixed points The link between outlier identification, robust statistics and cluster analysis is mentioned first by Hampel, Ronchetti, Rousseeuw and Stahel (1986, p. 46) to my knowledge. Robust statistics often deals with the location of a large homogeneous main part of the data in presence of outliers, which may be produced by mechanisms different from the rest, and which should not largely affect the estimation of the main part. Cluster analysis more ....
Hampel, F. R., Ronchetto, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986): Robust Statistics. The Approach Based on Influence Functions, Wiley, New York.
....distribution of Huber, see [5] We refer the reader to that paper for some theory concerning its optimality. An additional problem occurs when an explanatory variable x i is very different from the rest. Such an observation is highly influential even with the least favorable distribution, cf. [4], Section 6.2. Our way to deal with this problem is to employ in addition a varying scale depending on how far out x i is. Thus in our model the r i s are independent and have the density f(r i ) 1 Gamma ) p 2oe) Gamma1 w i expf Gammaae c ( w i r i oe )g = w i oe f 0 ( w i r i ....
F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw and W.A. Stahel. Robust Statistics, The Approach Based On Influence Functions. Wiley, New York, 1986.
....iconic correlation algorithms can be implemented for real time performance on a parallel DSP like the C80. However, its performance is very limited if the object being tracked change its appearance while the model is kept constant. This is due, both to the characteristics of the matching measure [10] and to the static nature of the model that does not track the variations in the visual appearance of the area being tracked. Obviously, to accomplish with the second condition a mechanism is needed to update the model. To deal with this problem, we have developed a new algorithm based in the ....
F.R.Hampel, E.M. Ronchetti, P.J. Rousseeuw, and W.A. Stahel. Robust Statistics. The Approach Based on Influence Functions. John Wiley & Sons Inc., New York, 1986.
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R. Hampel, E.M. Ronchetti, P.J. Rousseeuw and W.A. Stahel, Robust Statistics. The approach Based on InfluenceFunction, Wiley & Sons --- New York, 1986.
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R. Hampel, E.M. Ronchetti, P.J. Rousseeuw and W.A. Stahel, Robust Statistics. The approach Based on Influence Function, Wiley & Sons --- New York, 1986.
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F. R. Hampel, E. M. Ronchetti, P. J. Rousseleuw, and W. A. Stahel, Robust Statistics, the Approach based on influence Function, John Wiley & Sons, New York, 1986.
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Hampel, F. R.; Ronchetti, E. M.; Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics, the Approach Based on Influence Functions. John Wiley, New York.
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Hampel, F. R.; Ronchetti, E. M.; Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics, the Approach Based on Influence Functions. John Wiley, New York.
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F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw and W.A. Stahel, Robust Statistics, the Approach Based on Influence Functions, John Wiley & Sons, 1986.
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F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw, W. A. Stahel, Robust Statistics. The Approach Based on Influence Functions, Wiley, New York, 1986. DRAFT
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