On strong laws for generalized L-statistics with dependent data
Gilat, David ; Helmers, Roelof
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 187-192 / Harvested from Czech Digital Mathematics Library
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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).

Publié le : 1997-01-01
Classification:  28D05,  60F15,  60G10,  62G20,  62G30 
@article{118915,
     author = {David Gilat and Roelof Helmers},
     title = {On strong laws for generalized L-statistics with dependent data},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {187-192},
     zbl = {0889.60029},
     mrnumber = {1455483},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118915}
}

Gilat, David; Helmers, Roelof. On strong laws for generalized L-statistics with dependent data. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 187-192. http://gdmltest.u-ga.fr/item/118915/

Aaronson J. An ergodic theorem with large normalising constants, Israel J. Math. 38 (1981), 182-188. (1981) | MR 0605376 | Zbl 0468.60036

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) | MR 1363941 | Zbl 0863.60032

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) | MR 0952995 | Zbl 0631.60032

Van Zwet W.R. A strong law for linear functions of order statistics, Ann. Probab. 8 (1980), 986-990. (1980) | MR 0586781 | Zbl 0448.60025