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A note on the empirical distribution of dependent random variables

Author

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  • Hanson, D. L.
  • Li, Gang

Abstract

Let be an adapted stochastic sequence. Let . In stochastic approximation and various other sequential procedures, the question of whether arises. For each t, Dn(t) converges to 0 a.s., and by the Glivenko-Cantelli theorem (1) holds if {Yn} is i.i.d. We give an example showing that without the assumption of independence (1) might fail to hold.

Suggested Citation

  • Hanson, D. L. & Li, Gang, 1997. "A note on the empirical distribution of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 337-340, June.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:4:p:337-340
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    Cited by:

    1. Berti, Patrizia & Rigo, Pietro, 2002. "A uniform limit theorem for predictive distributions," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 113-120, January.

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