Continuity of scale parameter estimators with respect to stochastic orders

• Autorzy: Bartoszewicz, J. , Frąszczak, M.
• Języki publikacji: EN

Abstrakty

EN

Lehmann and Rojo [8] proposed a concept of invariance of stochastic orders and related probability metrics with respect to increasing transformations of random variables. Bartoszewicz and Benduch [3] and Bartoszewicz and Frąszczak [4] applied a concept of Lehmann and Rojo to new settings. In the paper these results are applied to the problem of robustness in the sense of Zieliński [11], [12]. Metrics related to some stochastic orders are used to study the continuity (robustness) of scale parameter estimators when contaminations of the models are generated by stochastic orders. The exponential model is considered in detail.

Słowa kluczowe

EN

life distribution; partial order; order statistics; probability metrics; robustness

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2012
• Tom: Vol. 32, Fasc. 1
• Strony: 57--67
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Bartoszewicz, J.

• Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland,

autor

Frąszczak, M.

• Institute of Genetics, Wrocław University of Environmental and Life Sciences, ul. Kożuchowska 7, 51-631 Wrocław, Poland,

Bibliografia

• [1] J. Bartoszewicz, Bias-robust estimation of scale parameter, Probab. Math. Statist. 7 (1986), pp. 103-113.
• [2] J. Bartoszewicz, Bias-robust estimates based on order statistics and spacings in the exponential model, Zastos. Mat. 19 (1987), pp. 57-63.
• [3] J. Bartoszewicz and M. Benduch, Some properties of the generalized TTT transform, J. Statist. Plann. Inference 139 (2009), pp. 2208-2217.
• [4] J. Bartoszewicz and M. Frąszczak, Invariance of relative inverse function orderings under compositions of distributions, 2011, submitted.
• [5] M. Benduch-Frąszczak, Some properties of Marshall-Olkin family of distributions, Appl. Math. (Warsaw) 37 (2010), pp. 247-256.
• [6] F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw and W. A. Stahel, Robust Statistics. The Approach Based on Influence Functions, Wiley, 1986.
• [7] P. J. Huber, Robust Statistics, Wiley, 1981.
• [8] E. L. Lehmann and J. Rojo, Invariant directional orderings, Ann. Statist. 20 (1992), pp. 2100-2110.
• [9] A. W. Marshall and I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84 (1997), pp. 641-652.
• [10] M. Shaked and J. G. Shanthikumar, Stochastic Orders, Springer, 2007.
• [11] R. Zieliński, Robustness: a quantitative approach, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 25 (1977), pp. 1281-1286.
• [12] R. Zieliński, Robust statistical procedures: A general approach, Lecture Notes in Math. 982, Springer, 1983, pp. 283-295.