One of the characterization problems of statistics is reconstruction of types when observations can have different location and/or scale parameters. In these cases, invariant statistics are used, and one of the main problems is uniqueness and stability of the reconstruction. There are a number of works devoted to this problem. In this article, we obtain a new estimate of stability of the normal type. It improves previously obtained estimates.
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A. M. Kagan and L.B. Klebanov, “Estimation of the stability in the problem of reconstructing the additive type of a distribution,” Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI), 61, No. 136, 68–74 (1976).
L. B. Klebanov, “More on estimating the stability in the problem of reconstructing the additive type of a distribution,” Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI), 87, 74–78 (1979).
L. D. Meshalkin and B. A. Rogozin, “An estimate of the distance between distribution functions from the closeness of their characteristic functions and its application to the central limit theorem,” in: Limit Theorems of Probability Theory, Tashkent (1963), pp. 49–55.
A. A. Petrov, “Verification of statistical hypotheses on the type of a distribution based on small samples,” Theor. Prob. Appl.1, No. 2, 248–271 (1956).
Yu.V. Prokhorov, “A characterization of a class of probability distributions by the distributions of certain statistics,” Theor. Prob. Appl., 10, No. 4, 479–487 (1965).
A.P. Ushakova, “Estimates of stability of characterization of additive types of distributions,” J. Math. Sci., 89, No. 5, 1582–1589 (1998).
A. A. Zinger, “On a problem of A.N. Kolmogorov,” Vestn. Leningrad. Univ., 11, No. 1, 53–56 (1956).
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Proceedings of the XXXV International Seminar on Stability Problems for Stochastic Models, Perm, Russia, September 24–28, 2018. Part I.
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Ushakova, A.P., Ushakov, N.G. An Estimate of Stability of Reconstruction of the Normal Distribution Type. J Math Sci 246, 560–564 (2020). https://doi.org/10.1007/s10958-020-04760-x
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DOI: https://doi.org/10.1007/s10958-020-04760-x