• Communications for Statistical Applications and Methods
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• 제13권3호
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• pp.513-524
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• 2006

In this paper, we introduce a new notions of conditionally weak dependence and we study their properties, preservation of the conditionally weak independent and positive and negative quadrant dependent(CWQD) property under mixtures, limits, closure under convex combinations, and their interrelationships. Furthermore, we extend multivariate stochastic dependence to stronger conditions of dependence.

• 호남수학학술지
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• 제27권2호
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• pp.301-315
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• 2005

Let $\{A_u,\;u=0,\;1,\;2,\;{\cdots}\}$ be a sequence of coefficient matrices such that ${\sum}_{u=0}^{\infty}{\parallel}A_u{\parallel}<{\infty}$ and ${\sum}_{u=0}^{\infty}\;A_u{\neq}O_{m{\times}m}$, where for any $m{\times}m(m{\geq}1)$, matrix $A=(a_{ij})$, ${\parallel}A{\parallel}={\sum}_{i=1}^m{\sum}_{j=1}^m{\mid}a_{ij}{\mid}$ and $O_{m{\times}m}$ denotes the $m{\times}m$ zero matrix. In this paper, a functional central limit theorem is derived for a stationary m-dimensional linear process ${\mathbb{X}}_t$ of the form ${\mathbb{X}_t}={\sum}_{u=0}^{\infty}A_u{\mathbb{Z}_{t-u}}$, where $\{\mathbb{Z}_t,\;t=0,\;{\pm}1,\;{\pm}2,\;{\cdots}\}$ is a stationary sequence of linearly positive quadrant dependent m-dimensional random vectors with $E({\mathbb{Z}_t})={{\mathbb{O}}$ and $E{\parallel}{\mathbb{Z}_t}{\parallel}^2<{\infty}$.