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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:
60F15Strong limit theorems
62G05Nonparametric estimation