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Trace inequalities for mixtures of Markov chains

Published online by Cambridge University Press:  01 July 2016

Burton Singer  and
Seymour Spilerman
Burton Singer
Affiliation:
Columbia University, New York
Seymour Spilerman
Affiliation:
Russell Sage Foundation, New York
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Abstract

In a wide variety of multi-wave panel studies in economics and sociology, comparisons between the observed transition matrices and predictions of them based on time-homogeneous Markov chains have revealed a special kind of discrepancy: the trace of the observed matrices tends to be larger than the trace of the predicted matrices. A common explanation for this discrepancy has been via mixtures of Markov chains.

Specializing to mixtures of Markov semi-groups of the form

we exhibit classes of stochastic matrices M, probability measures µ and time intervals Δ such that for k = 2, 3 and 4. These examples contradict the substantial literature which suggests — implicitly — that the above inequality should be reversed for general mixtures of Markov semi-groups.

Keywords

MIXTUREMARKOV CHAINTRACE INEQUALITIESSOCIOLOGYPANEL STUDY
Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 4 , December 1977 , pp. 747 - 764
Copyright
Copyright © Applied Probability Trust 1977 

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