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Marcinkiewicz strong laws for linear statistics. (English) Zbl 0960.60026
Summary: Strong laws are established for linear statistics that are weighted sums of a random sample. We show extensions of the Marcinkiewicz-Zygmund strong law under certain moment conditions on both the weights and the distribution. These complement the results of J. Cuzick [J. Theor. Probab. 8, No. 3, 625-641 (1995; Zbl 0833.60031)] and the authors and C. H. Zhang [Stat. Sin. 7, 923-928 (1997)].

MSC:
60F15 Strong limit theorems
62G05 Nonparametric estimation
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[1] Bai, Z.D., Cheng, P.E., Zhang, C.H., 1997. An extension of the Hardy-Littlewood strong law. Statist. Sinica, 923-928. · Zbl 1067.60501
[2] Cheng, P.E., A note on strong convergence rates in nonparametric regression, Statist. probab. lett., 24, 357-364, (1995) · Zbl 0835.62046
[3] Cuzick, J., A strong law for weighted sums of i.i.d. random variables, J. theoret. probab, 8, 625-641, (1995) · Zbl 0833.60031
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