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Marcinkiewicz strong laws for linear statistics

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  • Bai, Z. D.
  • Cheng, Philip E.

Abstract

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 Cuzick (1995, J. Theoret. Probab. 8, 625-641) and Bai et al. (1997, Statist. Sinica, 923-928).

Suggested Citation

  • Bai, Z. D. & Cheng, Philip E., 2000. "Marcinkiewicz strong laws for linear statistics," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 105-112, January.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:2:p:105-112
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    References listed on IDEAS

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    1. Cheng, Philip E., 1995. "A note on strong convergence rates in nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 357-364, September.
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    Cited by:

    1. Pingyan, Chen & Shixin, Gan, 2007. "Limiting behavior of weighted sums of i.i.d. random variables," Statistics & Probability Letters, Elsevier, vol. 77(16), pages 1589-1599, October.
    2. Yi Wu & Xuejun Wang & Aiting Shen, 2021. "Strong convergence properties for weighted sums of m-asymptotic negatively associated random variables and statistical applications," Statistical Papers, Springer, vol. 62(5), pages 2169-2194, October.
    3. Soo Sung, 2011. "On the strong convergence for weighted sums of random variables," Statistical Papers, Springer, vol. 52(2), pages 447-454, May.
    4. Shuxia Guo & Zhe Meng, 2023. "The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences under Sublinear Expectation," Mathematics, MDPI, vol. 11(23), pages 1-21, November.
    5. Yi Wu & Xuejun Wang & Aiting Shen, 2023. "Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-28, March.
    6. Sung, Soo Hak, 2001. "Strong laws for weighted sums of i.i.d. random variables," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 413-419, May.
    7. Di Hu & Pingyan Chen & Soo Hak Sung, 2017. "Strong laws for weighted sums of $$\psi $$ ψ -mixing random variables and applications in errors-in-variables regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 600-617, September.
    8. Wei Li & Pingyan Chen & Soo Hak Sung, 2016. "Complete Moment Convergence for Sung’s Type Weighted Sums of -Valued Random Elements," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-8, March.
    9. Chen, Pingyan & Chen, Ran, 2010. "A remark on LSL for weighted sums of i.i.d random elements," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1329-1334, September.
    10. Sung, Soo Hak, 2009. "A law of the single logarithm for weighted sums of i.i.d. random elements," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1351-1357, May.
    11. Guang-hui Cai, 2008. "Strong laws for weighted sums of NA random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 323-331, November.

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