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Vajda, Igor

Asymptotic efficiency and robustness of D-estimators. (English) Zbl 0599.62039

Kybernetika 20, 358-375 (1984).
Asymptotic normality of standard, weak, and directed D-estimators investigated by the author in ibid. 20, 189-208, 283-303 (1984; Zbl 0558.62026 and the preceding review, Zbl 0599.62038, respectively) is established and influence curves are derived, all under the assumption of vector-valued parameter spaces. Asymptotic variance matrices of estimators under consideration are expressed as variances of the corresponding multidimensional influence curves. Conditions of asymptotic efficiency are established as well.

Cited in 1 Review
Cited in 1 Document

MSC:

62F12 Asymptotic properties of parametric estimators
62F35 Robustness and adaptive procedures (parametric inference)
62G20 Asymptotic properties of nonparametric inference
62H12 Estimation in multivariate analysis

Keywords:

robustness; weak D-estimators; Asymptotic normality; directed D- estimators; influence curves; vector-valued parameter spaces; Asymptotic variance matrices; asymptotic efficiency

Citations:

Zbl 0558.62026; Zbl 0599.62038
PDFBibTeX XMLCite
\textit{I. Vajda}, Kybernetika 20, 358--375 (1984; Zbl 0599.62039)
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References:

[1] J. Anděl: Mathematical Statistics. (in Czech). SNTL - Alfa, Praha-Bratislava 1978.
[2] D. F. Andrews P. J. Bickel F. R. Hampel P. J. Huber W. H. Rogers, J. W. Turkey: Robust Estimates of Location. Princeton Univ. Press, Princeton 1972. · Zbl 0254.62001 · doi:10.1515/9781400867011
[3] D. D. Boos: Minimum distance estimators for location and goodness of fit. J. Amer. Statist. Assoc. 76 (1981), 663-670. · Zbl 0475.62030 · doi:10.2307/2287527
[4] J. Grim: An algorithm for maximizing a finite sum of positive functions and its application to cluster analysis. Problems Control Inform. Theory 10 (1981), 427-437. · Zbl 0476.65100
[5] F. Hampel: The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69 (1974), 383-393. · Zbl 0305.62031 · doi:10.2307/2285666
[6] P. J. Huber: Robust estimation of a location parameter. Ann. Math. Statist. 35 (1964), 73-101. · Zbl 0136.39805 · doi:10.1214/aoms/1177703732
[7] J. W. Tukey: Exploratory Data Analysis. Addison-Wesley, Reading 1970.
[8] I. Vajda: Minimum divergence principle in statistical estimation. Statistics and Decisions 2 (1984), to appear. · Zbl 0558.62004
[9] I. Vajda: Motivation, existence and equivariance of D-estimators. Kybernetika 20 (1984), 3, 189-208. · Zbl 0558.62026
[10] I. Vajda: Consistency of D-estimators. Kybernetika 20 (1984), 4, 283-303. · Zbl 0599.62038
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