A Poisson limit theorem for incomplete symmetric statistics
- 1 March 1983
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 20 (1) , 47-60
- https://doi.org/10.2307/3213719
Abstract
Silverman and Brown (1978) have derived Poisson limit theorems for certain sequences of symmetric statistics, based on a sample of independent identically distributed random variables. In this paper an incomplete version of these statistics is considered and a Poisson limit result shown to hold. The powers of some tests based on the incomplete statistic are investigated and the main results of the paper are used to simplify the derivations of the asymptotic distributions of some statistics previously published in the literature.Keywords
This publication has 19 references indexed in Scilit:
- The Asymptotic Distribution of the Scan Statistic Under UniformityThe Annals of Probability, 1980
- Quick tests for spatial interactionBiometrika, 1978
- Limit theorems for weakly exchangeable arraysMathematical Proceedings of the Cambridge Philosophical Society, 1978
- Short distances, flat triangles and Poisson limitsJournal of Applied Probability, 1978
- Two Applications of a Poisson Approximation for Dependent EventsThe Annals of Probability, 1977
- THE MINIMUM OF HIGHER ORDER GAPSAustralian Journal of Statistics, 1977
- On some properties of the scan statistic on the circle and the lineJournal of Applied Probability, 1977
- Some properties of incomplete U-statisticsBiometrika, 1976
- The Distribution of the Size of the Maximum Cluster of Points on a LineJournal of the American Statistical Association, 1965
- A Class of Statistics with Asymptotically Normal DistributionThe Annals of Mathematical Statistics, 1948