Abstract
Necessary and sufficient conditions are derived for uniform local asymptotic normality of experiments generated by a sequence of independent homogeneous observations.
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Literature cited
L. LeCam, “Locally asymptotically normal families of distributions,” Univ. Calif. Publ. Stat.,3, No. 2, 37–48.
J. Hajek, “A characterization of limiting distributions of regular estimates,” Z. Wahrscheinlichkeitstheorie Verw. Geb.,14, 323–330 (1970).
J. Hajek, “Local asymptotic minimax and admissibility in estimation,” Proc. 6th Berkeley Symp. on Math. Stat. and Prob., Vol. 1 (1972), pp. 175–194.
L. LeCam, “On some results of J. Hajek concerning asymptotic normality,” in: Hajek's Memorial Volume, Prague (in print).
B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley (1968).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 74, pp. 108–117, 1977.
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Ibragimov, I.A., Khas'minskii, R.Z. A uniform condition of local asymptotic normality. J Math Sci 34, 1427–1432 (1986). https://doi.org/10.1007/BF01085010
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DOI: https://doi.org/10.1007/BF01085010