Law of large numbers for the subseries values of a statistic from a stationary sequence. (English) Zbl 0643.62026
Summary: For estimating the theoretical moments of a general statistic, we propose computing “subseries values” of the statistic as replicates. The user need not know the dependence model or marginal distributions of the underlying stationary sequence in order to apply this technique. We prove consistency of the moment estimator under very mild assumptions.
References:
| [1] | DOI: 10.1214/aop/1176992377 · Zbl 0609.62025 · doi:10.1214/aop/1176992377 |
| [2] | Cnow Y. S, Probability Theory (1978) |
| [3] | Gastwirth J.L., Ann. Statist 3 pp 809– (195) · Zbl 0318.62016 · doi:10.1214/aos/1176343184 |
| [4] | Ibraotmov I. A, Independent and Stationary Sequences of Random Variables (1971) |
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