Strong laws for weighted sums of $$\psi $$ ψ -mixing random variables and applications in errors-in-variables regression models

Strong laws for weighted sums of $$\psi $$ ψ -mixing random variables and applications in... In this paper, we establish strong laws for weighted sums of identically distributed $$\psi $$ ψ -mixing random variables without any conditions on mixing rate. The classical Kolmogorov strong law of large numbers is extended to weighted sums of $$\psi $$ ψ -mixing random variables. Two types of weights are considered for the weighted sums. These results are applied to the least-squares estimators in the simple linear errors-in-variables regression model when the errors are $$\psi $$ ψ -mixing random vectors. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png TEST Springer Journals

Strong laws for weighted sums of $$\psi $$ ψ -mixing random variables and applications in errors-in-variables regression models

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Sociedad de Estadística e Investigación Operativa
Subject
Statistics; Statistics, general; Statistical Theory and Methods
ISSN
1133-0686
eISSN
1863-8260
D.O.I.
10.1007/s11749-017-0526-6
Publisher site
See Article on Publisher Site

Abstract

In this paper, we establish strong laws for weighted sums of identically distributed $$\psi $$ ψ -mixing random variables without any conditions on mixing rate. The classical Kolmogorov strong law of large numbers is extended to weighted sums of $$\psi $$ ψ -mixing random variables. Two types of weights are considered for the weighted sums. These results are applied to the least-squares estimators in the simple linear errors-in-variables regression model when the errors are $$\psi $$ ψ -mixing random vectors.

Journal

TESTSpringer Journals

Published: Feb 9, 2017

References

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