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A CENTRAL LIMIT THEOREM FOR GENERAL WEIGHTED SUM OF LNQD RANDOM VARIABLES AND ITS APPLICATION

  • KIM, HYUN-CHULL (Division of Computer and Information Science Daebul University) ;
  • KIM, TAE-SUNG (Division of Mathematics and Informational Statistics and Institute of Basic Natural Science WonKwang University)
  • Published : 2005.07.01

Abstract

In this paper we derive the central limit theorem for ${\sum}_{i=1}^n\;a_{ni}\xi_i$, where ${a_{ni},\;1\;{\leq}\;i\;{\leq}\;n}$ is a triangular array of nonnegative numbers such that $sup_n{\sum}_{i=1}^n\;a_{ni}^2\;<\;{\infty},\;max_{1{\leq}i{\leq}n}a_{ni}{\rightarrow}0\;as\;n\;{\rightarrow}\;{\infty}\;and\;\xi'_i\;s$ are a linearly negative quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process $X_n\;=\;\sum_{j=-\infty}^\infty\;a_k+_j{\xi}_j$.

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Cited by

  1. On the Exponential Inequality for Weighted Sums of a Class of Linearly Negative Quadrant Dependent Random Variables vol.2014, 2014, https://doi.org/10.1155/2014/748242