On strong laws for generalized L-statistics with dependent data

David Gilat; Roelof Helmers

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 1, page 187-192
  • ISSN: 0010-2628

Abstract

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It is pointed out that a strong law of large numbers for L-statistics established by van Zwet (1980) for i.i.d. sequences, remains valid for stationary ergodic data. When the underlying process is weakly Bernoulli, the result extends even to generalized L-statistics considered in Helmers et al. (1988).

How to cite

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Gilat, David, and Helmers, Roelof. "On strong laws for generalized L-statistics with dependent data." Commentationes Mathematicae Universitatis Carolinae 38.1 (1997): 187-192. <http://eudml.org/doc/248100>.

@article{Gilat1997,
abstract = {It is pointed out that a strong law of large numbers for L-statistics established by van Zwet (1980) for i.i.d. sequences, remains valid for stationary ergodic data. When the underlying process is weakly Bernoulli, the result extends even to generalized L-statistics considered in Helmers et al. (1988).},
author = {Gilat, David, Helmers, Roelof},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {L-statistic; GL-statistic; strong law of large numbers; stationary ergodic process; L-statistic; GL-statistic; strong law of large numbers; stationary ergodic process},
language = {eng},
number = {1},
pages = {187-192},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On strong laws for generalized L-statistics with dependent data},
url = {http://eudml.org/doc/248100},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Gilat, David
AU - Helmers, Roelof
TI - On strong laws for generalized L-statistics with dependent data
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 1
SP - 187
EP - 192
AB - It is pointed out that a strong law of large numbers for L-statistics established by van Zwet (1980) for i.i.d. sequences, remains valid for stationary ergodic data. When the underlying process is weakly Bernoulli, the result extends even to generalized L-statistics considered in Helmers et al. (1988).
LA - eng
KW - L-statistic; GL-statistic; strong law of large numbers; stationary ergodic process; L-statistic; GL-statistic; strong law of large numbers; stationary ergodic process
UR - http://eudml.org/doc/248100
ER -

References

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  1. Aaronson J., An ergodic theorem with large normalising constants, Israel J. Math. 38 (1981), 182-188. (1981) Zbl0468.60036MR0605376
  2. Aaronson J., Burton R., Dehling H., Gilat D., Hill T., Weiss B., Strong laws for L- and U-statistics, Trans. Am. Math. Society 348 (1996), 2845-2866. (1996) Zbl0863.60032MR1363941
  3. Helmers R., Janssen P., Serfling R., Glivenko-Cantelli properties of some generalized empirical df's and strong convergence of generalized L-statistics, Probab. Th. Rel. Fields 79 (1988), 75-93. (1988) Zbl0631.60032MR0952995
  4. van Zwet W.R., A strong law for linear functions of order statistics, Ann. Probab. 8 (1980), 986-990. (1980) Zbl0448.60025MR0586781

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