Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables

For arrays of rowwise pairwise negative quadrant dependent random variables, conditions are provided under which weighted averages converge in mean to 0 thereby extending a result of Chandra, and conditions are also provided under which normed and centered row sums converge in mean to 0. These resul...

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Detalles Bibliográficos
Autores principales: Chandra, Tapas K., Li, Deli, Rosalsky, Andrew
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6132388/
https://www.ncbi.nlm.nih.gov/pubmed/30839650
http://dx.doi.org/10.1186/s13660-018-1811-y
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author Chandra, Tapas K.
Li, Deli
Rosalsky, Andrew
author_facet Chandra, Tapas K.
Li, Deli
Rosalsky, Andrew
author_sort Chandra, Tapas K.
collection PubMed
description For arrays of rowwise pairwise negative quadrant dependent random variables, conditions are provided under which weighted averages converge in mean to 0 thereby extending a result of Chandra, and conditions are also provided under which normed and centered row sums converge in mean to 0. These results are new even if the random variables in each row of the array are independent. Examples are provided showing (i) that the results can fail if the rowwise pairwise negative quadrant dependent hypotheses are dispensed with, and (ii) that almost sure convergence does not necessarily hold.
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spelling pubmed-61323882018-09-14 Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables Chandra, Tapas K. Li, Deli Rosalsky, Andrew J Inequal Appl Research For arrays of rowwise pairwise negative quadrant dependent random variables, conditions are provided under which weighted averages converge in mean to 0 thereby extending a result of Chandra, and conditions are also provided under which normed and centered row sums converge in mean to 0. These results are new even if the random variables in each row of the array are independent. Examples are provided showing (i) that the results can fail if the rowwise pairwise negative quadrant dependent hypotheses are dispensed with, and (ii) that almost sure convergence does not necessarily hold. Springer International Publishing 2018-08-23 2018 /pmc/articles/PMC6132388/ /pubmed/30839650 http://dx.doi.org/10.1186/s13660-018-1811-y Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Chandra, Tapas K.
Li, Deli
Rosalsky, Andrew
Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables
title Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables
title_full Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables
title_fullStr Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables
title_full_unstemmed Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables
title_short Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables
title_sort some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6132388/
https://www.ncbi.nlm.nih.gov/pubmed/30839650
http://dx.doi.org/10.1186/s13660-018-1811-y
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