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Modelling hierarchical systems by a continuous-time homogeneous Markov chain using two-wave panel data

Part of: Nonparametric inference Inference from stochastic processes Markov processes Applications

Published online by Cambridge University Press:  14 July 2016

Philippe Carette
Philippe Carette*
Affiliation:
Vrije Universiteit Brussel
*
∗Postal address: Center for Manpower Planning, Pleinlaan 2, B-1050 Brussel, Belgium. Email address: phcarett@vub.ac.be.
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Abstract

An open hierarchical (manpower) system divided into a totally ordered set of k grades is discussed. The transitions occur only from one grade to the next or to an additional (k+1)th grade representing the external environment of the system. The model used to describe the dynamics of the system is a continuous-time homogeneous Markov chain with k+1 states and infinitesimal generator R = (rij) satisfying rij = 0 if i > j or i + 1 < j ≤ k (i, j = 1,…,k+1), the transition matrix P between times 0 and 1 being P = expR. In this paper, two-wave panel data about the hierarchical system are considered and the resulting fact that, in general, the maximum-likelihood estimated transition matrix cannot be written as an exponential of an infinitesimal generator R having the form described above. The purpose of this paper is to investigate when this can be ascribed to the effect of sampling variability.

Keywords

Continuous-time Markov chainembedding problemstochastic matrixpanel datainference

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces 62M02: Markov processes
Secondary: 62G10: Hypothesis testing 62P25: Applications to social sciences
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 644 - 653
Copyright
Copyright © Applied Probability Trust 1999 

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