• Title, Summary, Keyword: Central limit theorem

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THE CENTRAL LIMIT THEOREMS FOR THE MULTIVARIATE LINEAR PROCESS GENERATED BY WEAKLY ASSOCIATED RANDOM VECTORS

  • Kim, Tae-Sung;Ko, Mi-Hwa
    • Journal of the Korean Statistical Society
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    • v.32 no.1
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    • pp.11-20
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    • 2003
  • Let{Xt}be an m-dimensional linear process of the form (equation omitted), where{Zt}is a sequence of stationary m-dimensional weakly associated random vectors with EZt = O and E∥Zt∥$^2$$\infty$. We Prove central limit theorems for multivariate linear processes generated by weakly associated random vectors. Our results also imply a functional central limit theorem.

A FUNCTIONAL CENTRAL LIMIT THEOREM FOR POSITIVELY DEPENDENT SEQUENCES

  • KIM, TAE-SUNG;KIM, HYUN-CHULL
    • Honam Mathematical Journal
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    • v.16 no.1
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    • pp.111-117
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    • 1994
  • In this note we prove a functional central. limit theorem for LPQD sequences, statisfying some moment conditions. No stationarity is required. Our results imply an extension of Birkel's functional central limit theorem for associated processt'S to an LPQD sequence and an improvement of Birkel's functional central limit theorem for LPQD sequences.

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Computer Simulation Program for Central Limit Theorem - Dynamic MS Excel Program -

  • Choi, Hyun-Seok;Kim, Tae-Yoon
    • Journal of the Korean Data and Information Science Society
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    • v.16 no.2
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    • pp.359-369
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    • 2005
  • Central limit theorem is known as one of the most important limit theorem in statistics and probability. This paper provides a dynamic MS Excel program that demonstrates computer simulation of various types of central limit theorems. Our result will be of great use for better understanding of central limit theorems.

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A Central Limit Theorem for a Stationary Linear Process Generated by Linearly Positive Quadrant Dependent Process

  • Kim, Tae-Sung;Ko, Mi-Hwa
    • Communications for Statistical Applications and Methods
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    • v.8 no.1
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    • pp.153-158
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    • 2001
  • A central limit theorem is obtained for stationary linear process of the form -Equations. See Full-text-, where {$\varepsilon$$_{t}$} is a strictly stationary sequence of linearly positive quadrant dependent random variables with E$\varepsilon$$_{t}$=0, E$\varepsilon$$^2$$_{t}$<$\infty$ and { $a_{j}$} is a sequence of real numbers with -Equations. See Full-text- we also derive a functional central limit theorem for this linear process.ocess.s.

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A functional central limit theorem for positively dependent random vectors

  • Kim, Tae-Sung;Baek, Jong-Il
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.707-714
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    • 1995
  • In this note, we extend the concepts of linearly positive quadrant dependence to the random vectors and prove a functional central limit theorem for positively quadrant dependent sequence of $R^d$-valued or separable Hilbert space valued random elements which satisfy a covariance summability condition. This result is an extension of a functional central limit theorem for weakly associated random vectors of Burton et al. to positive quadrant dependence case.

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A Central Limit Theorem for the Linear Process in a Hilbert Space under Negative Association

  • Ko, Mi-Hwa
    • Communications for Statistical Applications and Methods
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    • v.16 no.4
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    • pp.687-696
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    • 2009
  • We prove a central limit theorem for the negatively associated random variables in a Hilbert space and extend this result to the linear process generated by negatively associated random variables in a Hilbert space. Our result implies an extension of the central limit theorem for the linear process in a real space under negative association to a simplest case of infinite dimensional Hilbert space.

CONDITIONAL CENTRAL LIMIT THEOREMS FOR A SEQUENCE OF CONDITIONAL INDEPENDENT RANDOM VARIABLES

  • Yuan, De-Mei;Wei, Li-Ran;Lei, Lan
    • Journal of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.1-15
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    • 2014
  • A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.