A note on central limit theorems for lattice models
type: Item
instance of: scholarly article
title: A note on central limit theorems for lattice models
zbMATH Open document ID: 0954.60013
DOI: 10.1016/S0378-3758(99)00103-2
author: S. G. Sajjan
published in: Journal of Statistical Planning and Inference
publication date: 2001-01-25T00:00:00Z
review text: Let \(\{U_{ts}\}\), \(t=1,\dots,m_1\), \(s=1,\dots,m_2\), be a process defined on a two-dimensional lattice. Let \(m_1\), \(m_2\) be nonnegative integers. Assume that \(\{U_{ts}\}\) is stationary. The author defines that \(\{U_{ts}\}\) is \((m_1, m_2)\)-dependent if the sets \(\{U_{ij}, i\leq t, j\leq s\}\) and \(\{U_{ij}, i\geq t+m_1+1 \text{ or } j\geq s+m_2 +1\}\) are independent for each \((t,s)\). A central limit theorem (CLT) for \((m_1, m_2)\)-dependent processes is derived and generalized to a weighted CLT. Results of a simulation study are presented.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 1423775
zbMATH Keywords: time series
zbMATH Keywords: lattice processes
zbMATH Keywords: \(m\)-dependent processes
zbMATH Keywords: spatial processes
zbMATH Keywords: asymptotics
reviewed by: Jiří Anděl
describes a project that uses: spatial
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1423775