| Title:
|
On strong laws for generalized L-statistics with dependent data (English) |
| Author:
|
Gilat, David |
| Author:
|
Helmers, Roelof |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
187-192 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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). (English) |
| Keyword:
|
L-statistic |
| Keyword:
|
GL-statistic |
| Keyword:
|
strong law of large numbers |
| Keyword:
|
stationary ergodic process |
| MSC:
|
28D05 |
| MSC:
|
60F15 |
| MSC:
|
60G10 |
| MSC:
|
62G20 |
| MSC:
|
62G30 |
| idZBL:
|
Zbl 0889.60029 |
| idMR:
|
MR1455483 |
| . |
| Date available:
|
2009-01-08T18:30:06Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118915 |
| . |
| Reference:
|
[1] Aaronson J.: An ergodic theorem with large normalising constants.Israel J. Math. 38 (1981), 182-188. Zbl 0468.60036, MR 0605376 |
| Reference:
|
[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. Zbl 0863.60032, MR 1363941 |
| Reference:
|
[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. Zbl 0631.60032, MR 0952995 |
| Reference:
|
[4] van Zwet W.R.: A strong law for linear functions of order statistics.Ann. Probab. 8 (1980), 986-990. Zbl 0448.60025, MR 0586781 |
| . |
