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Strong laws of large numbers for arrays of row-wise exchangeable random elements

Author

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  • Robert Lee Taylor
  • Ronald Frank Patterson

Abstract

Let { X n k , 1 ≤ k ≤ n , n ≤ 1 } be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence of n − 1 / p ∑ k = 1 n X n k , 1 ≤ p < 2 , is obtained under varying moment and distribution conditions on the random elements. In particular, strong laws of large numbers follow for triangular arrays of random elements in(Rademacher) type p separable Banach spaces. Consistency of the kernel density estimates can be obtained in this setting.

Suggested Citation

  • Robert Lee Taylor & Ronald Frank Patterson, 1985. "Strong laws of large numbers for arrays of row-wise exchangeable random elements," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 8, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:863212
    DOI: 10.1155/S0161171285000126
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    Cited by:

    1. Li Guan & Juan Wei & Hui Min & Junfei Zhang, 2021. "The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    2. Izmirlian, Grant, 2020. "Strong consistency and asymptotic normality for quantities related to the Benjamini–Hochberg false discovery rate procedure," Statistics & Probability Letters, Elsevier, vol. 160(C).

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