Abstract
The present paper is a continuation of the authors' work [1]. As in [1], we consider a sample from a general collection with distribution density f(x− θ) depending on the shift parameter θ. In contrast to [1] it is assumed that the function f(x) is unbounded in a neighborhood of points x1,h., xN where it can be represented in the form (1.1). The main results assert that for the Bayes estimates tn the normalized differences n1/(1+α)(tn−θ) have a proper limit distribution.
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Literature cited
I. A. Ibragimov and R. Z. Khas'minskii, “The asymptotic behavior of statistical estimates of the shift parameter for samples with continuous density having singularities,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst.,41 (1974).
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 55, pp. 175–184, 1976.
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Ibragimov, I.A., Khas'minskii, R.Z. Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density. J Math Sci 16, 1035–1041 (1981). https://doi.org/10.1007/BF01676146
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DOI: https://doi.org/10.1007/BF01676146