The central limit theorem for m-dependent variables asymptotically stationary to second order
- 1 April 1954
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 50 (2) , 287-292
- https://doi.org/10.1017/s0305004100029340
Abstract
In a recent paper (3) the Lindeberg-Lévy theorem (2) was extended for certain types of stationary dependent variables. In the present paper mainly the same basic ideas as were used in (3) are employed to give central limit theorems for m-dependent scalar variables (a) stationary to second order and (b) asymptotically stationary to second order, the sufficient condition in each case being akin to the Linde-berg condition ((1), p. 57) for independent variables. The analogue of the main theorem for vector variables is given. An extension of the Lindeberg-Lévy theorem is derived.Keywords
This publication has 1 reference indexed in Scilit:
- Some probability limit theorems with statistical applicationsMathematical Proceedings of the Cambridge Philosophical Society, 1953