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Report, 2010

Maximum likelihood estimation in a discretely observed immigration-death process

Cronie, Ottmar; Yu, Jun


In order to nd the maximum likelihood (ML) estimator of the parameter pair governing the immigration-death process (a continuous time Markov chain) we derive its transition probabilities. The likelihood maximisation problem is reduced from two dimensions to one dimension. We also show the consistency and the asymptotic normality of the ML-estimator under an equidistant sampling scheme, given that the parameter pair lies in some compact subset of the positive part of the real plane. We thereafter evaluate, numerically, the behaviour of the estimator and we nally see how our ML-estimation can be applied to the so-called Renshaw-S??ärkk??ä growth interaction model; a spatiotemporal point process with time dependent interacting marks in which the immigration-death process controls the arrivals of new marked points as well as their potential life-times


Immigration-death process; transition probability; likelihood; consistency; asymptotic normality; spatio-temporal marked point process

Published in

Research report (Centre of Biostochastics)
2010, number: 2010:01, pages: 1-53
Publisher: Centre of Biostochastics, Swedish University of Agricultural Sciences

Authors' information

Cronie, Ottmar
Chalmers University of Technology
Yu, Jun
Swedish University of Agricultural Sciences, Department of Forest Economics

UKÄ Subject classification

Forest Science

URI (permanent link to this page)