Asymptotic properties of randomly indexed sequences of random variables
- 1 January 1981
- journal article
- Published by Wiley in The Canadian Journal of Statistics / La Revue Canadienne de Statistique
- Vol. 9 (1) , 101-107
- https://doi.org/10.2307/3315300
Abstract
Conditions are given for a randomly indexed sequence of random variables to converge weakly. The key concept employed is the so‐called generalized Anscombe condition. The results give a method of determining sequential stopping rules, which have the required accuracy of estimation of an unknown parameter in the case when the observations are not necessarily independent and identically distributed.Keywords
This publication has 10 references indexed in Scilit:
- Weak convergence of sequences of random elements with random indicesMathematical Proceedings of the Cambridge Philosophical Society, 1980
- On Mixing and Stability of Limit TheoremsThe Annals of Probability, 1978
- Weak convergence of randomly indexed sequences of random variablesMathematical Proceedings of the Cambridge Philosophical Society, 1978
- On the Asymptotic Distribution of the Sequences of Random Variables with Random IndicesThe Annals of Mathematical Statistics, 1971
- On the Asymptotic Theory of Fixed-Width Sequential Confidence Intervals for the MeanThe Annals of Mathematical Statistics, 1965
- On the Asymptotic Theory of Fixed-Size Sequential Confidence Bounds for Linear Regression ParametersThe Annals of Mathematical Statistics, 1965
- On the central limit theorem for the sum of a random number of independent random variablesProbability Theory and Related Fields, 1963
- On mixing sequences of setsActa Mathematica Hungarica, 1958
- Sequential EstimationJournal of the Royal Statistical Society Series B: Statistical Methodology, 1953
- Large-sample theory of sequential estimationMathematical Proceedings of the Cambridge Philosophical Society, 1952