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A note on two measures of dependence and mixing sequences

Published online by Cambridge University Press:  01 July 2016

Magda Peligrad
Magda Peligrad*
Affiliation:
University of Rome
*
∗Postal address: Istituto Mathematico ‘Guido Castelnuovo', Università di Roma, Piazzale Aldo Moro, Città Universitaria, 00100 Roma, Italy.
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Abstract

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In this note we establish an inequality between the maximal coefficient of correlation and the φ -mixing coefficient which is symmetric in its arguments. Motivated by this inequality, we introduce a mixing coefficient which is the product of two φ -mixing coefficients.

We also study an invariance principle under conditions imposed on this new mixing coefficient. As a consequence of this result it follows that the invariance principle holds when either the direct-time process or its time-reversed process is φ -mixing; when both processes are φ-mixing the invariance principle holds for sequences of L 2-integrable random variables under a mixing rate weaker than that used by Ibragimov.

Keywords

MAXIMAL COEFFICIENT OF CORRELATION

Information

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 15 , Issue 2 , June 1983, pp. 461 - 464
Copyright
Copyright © Applied Probability Trust 1983 

References

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