Back to Search
Start Over
The central limit theorem for m-dependent variables
- Source :
- Mathematical Proceedings of the Cambridge Philosophical Society. 51:92-95
- Publication Year :
- 1955
- Publisher :
- Cambridge University Press (CUP), 1955.
-
Abstract
- In a previous paper (4) central limit theorems were obtained for sequences of m-dependent random variables (r.v.'s) asymptotically stationary to second order, the sufficient conditions being akin to the Lindeberg condition (3). In this paper similar theorems are obtained for sequences of m-dependent r.v.'s with bounded variances and with the property that for large n, where s′n is the standard deviation of the nth partial sum of the sequence. The same basic ideas as in (4) are used, but the proofs have been simplified. The results of this paper are examined in relation to earlier ones of Hoeffding and Robbins(5) and of the author (4). The cases of identically distributed r.v.'s and of vector r.v.'s are mentioned.
Details
- ISSN :
- 14698064 and 03050041
- Volume :
- 51
- Database :
- OpenAIRE
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Accession number :
- edsair.doi...........cf3db5749335113ef2dd19c8cf5ebcd4