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

Title & Authors
A CENTRAL LIMIT THEOREM FOR GENERAL WEIGHTED SUM OF LNQD RANDOM VARIABLES AND ITS APPLICATION
KIM, HYUN-CHULL; KIM, TAE-SUNG;

Abstract
In this paper we derive the central limit theorem for $\small{{\sum}_{i=1}^n\;a_{ni}\xi_i}$, where $\small{{a_{ni},\;1\;{\leq}\;i\;{\leq}\;n}}$ 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 $\small{X_n\;=\;\sum_{j=-\infty}^\infty\;a_k+_j{\xi}_j}$.ĀĀ會ĀĀ�ﾖ⨀恡辣ĀĀĀ會ĀĀゕﾖ⨀냻㆗ЀĀЀ會ĀЀ袕ﾖ⨀僼㆗Ā؀會Ā؀ﾖ⨀삧Āࠀ會Āࠀ㢖ﾖ⨀퀝䚑Ā᐀會Ā᐀邖ﾖ⨀㠝䚑⤀Ā저會Ā저ﾖ⨀磺삧Ā᐀會Ā᐀䂗ﾖ⨀჻삧Ā᐀會Ā᐀颗ﾖ⨀恔㦔瀀ꀏ會Āﾖ⨀퀝䚑Ā᐀會Ā᐀䢘ﾖ⨀삤ᮠĀ㰀會Ā㰀ꂘﾖ⨀墥ᮠĀ㈀會Ā㈀ﾖ⨀ᮠĀ᐀
Keywords
central limit theorem;linear process;linearly negative quadrant dependent;uniformly integrable;triangular array;
Language
English
Cited by
1.
On the Exponential Inequality for Weighted Sums of a Class of Linearly Negative Quadrant Dependent Random Variables, The Scientific World Journal, 2014, 2014, 1
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