Statistical inference from set-valued observations

• Autorzy: Schreiber T.
• Języki publikacji: EN

Abstrakty

EN

Consider a random experiment whose true (unknown) outcome is modelled by a certain randomelementX and the available imprecise observations are modelled by some random set A such that X ∈ A almost surely. The purpose of the paper is to propose a statistical procedure for estimation of the real distribution of X. The asymptotic properties of the suggested procedure are then investigated in both nonparametric and parametric settings. So far, only the results for a finite sample space are available.

Słowa kluczowe

EN

statistical procedure for estimation; asymptotic properties

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 2
• Strony: 223--235
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Schreiber T.

• Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Toruń, Poland

Bibliografia

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• [2] P. Dupuis and R. S. Ellis, A Weak Convergence Approach to the Theory of Large Deviations,, Wiley, Chichester 1997.
• [3] I A. Ibrahimоv and R. Z. Khasminskii, Asymptotic Estimation Theory (in Russian), Nauka, Moscow 1979.
• [4] J.-Y. Jaffray, On the maximum of conditional entropy for upper / lower probabilities generated by random sets, in: Random Sets: Theory and Applications, J. Goutsias, R. P. S. Mahler and H. T. Nguyen (Eds.), The IMA Volumes in Mathematics and its Applications, Springer, New York 1997, pp. 105-127.
• [5] G. Matheron, Random Sets and Integral Geometry, Wiley, New York 1975.
• [6] A. Meyerowitz, F. Richman and E. Walker, Calculating maximum-entropy probability densities for belief functions, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 2, No. 4 (1994), pp. 377-389.
• [7] I. S. Molchanov, Limit Theorems for Unions of Random Closed Sets, Lecture Notes in Math. 1561, Springer, Berlin 1993.
• [8] T. Norberg, An ordered random set coupling, Probab. Theory Related Fields 37 (1992), pp. 161-163.
• [9] T. Norberg, On the existence of ordered couplings of random sets - with applications, Israel J. Math. 77 (1992), pp. 241-264.
• [10]R. Schneider, Convex bodies: the Brunn-Minkowski theory, Encyclopaedia Math. Appl. 44, Cambridge University Press, 1993.
• [11] A. W. van der Vaart and J. A. Wellner, Weak Convergence and Empirical Processes with Applications to Statistics, Springer, New York 1996.