Efficiency comparison of M-estimates for scale at t-distributions
Using Fisher's information fort-distributions, the absolute asymptotic efficiency of some M-estimates for scale with known location parameter is calculated and graphically illustrated. The compared estimators are the standard deviation S^sub *^, the mean absolute deviation, called mean deviatio...
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| Veröffentlicht in: | Statistical papers (Berlin, Germany) Germany), 2000-01, Vol.41 (1), p.53-64 |
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| description | Using Fisher's information fort-distributions, the absolute asymptotic efficiency of some M-estimates for scale with known location parameter is calculated and graphically illustrated. The compared estimators are the standard deviation S^sub *^, the mean absolute deviation, called mean deviation D^sub *^, the median absolute deviation, called MAD^sub *^, and some M-estimates for scale, one, which is very robust, and another one with high asymptotic efficiency fort-distributions close to the normal. The last one is considered with monotone (in the positive field) and with very late redescending χ-function too. Also the [sigma][hat]^sub *^-arch, an alternative and generalized excess measure defined as the double relative asymptotic variance of the underlying scale estimator [sigma][hat]^sub *^ in the previous paper, is calculated fort-distributions and graphically illustrated, because there is the relation that the higher the asymptotic efficiency of [sigma][hat]^sub *^ is, the lower is the corresponding [sigma][hat]^sub *^-arch. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1007/BF02925676 |
| format | Article |
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The compared estimators are the standard deviation S^sub *^, the mean absolute deviation, called mean deviation D^sub *^, the median absolute deviation, called MAD^sub *^, and some M-estimates for scale, one, which is very robust, and another one with high asymptotic efficiency fort-distributions close to the normal. The last one is considered with monotone (in the positive field) and with very late redescending χ-function too. Also the [sigma][hat]^sub *^-arch, an alternative and generalized excess measure defined as the double relative asymptotic variance of the underlying scale estimator [sigma][hat]^sub *^ in the previous paper, is calculated fort-distributions and graphically illustrated, because there is the relation that the higher the asymptotic efficiency of [sigma][hat]^sub *^ is, the lower is the corresponding [sigma][hat]^sub *^-arch. 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| subjects | Asymptotic methods Asymptotic properties Computational efficiency Computing time Deviation Efficiency Estimates Estimators Mathematical analysis Mean Normal distribution Random variables Standard deviation Variance |
| title | Efficiency comparison of M-estimates for scale at t-distributions |
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