Maximum likelihood estimation in a discretely observed immigration-death process
2010 (English)Report (Other academic)
In order to find 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 finally see how our ML-estimation can be applied to the so-called Renshaw-Särkkä growth interaction model; a spatio-temporal 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.
Place, publisher, year, edition, pages
Sveriges Lantbruksuniversitet, 2010. , 55 p.
, Research Report, Centre of Biostochastics, ISSN 1651-8543 ; 2010-1
Immigration-death process, M/M/-queue, transition probability, likelihood, consistency, asymptotic normality, spatio-temporal marked point process
Probability Theory and Statistics
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:umu:diva-63721OAI: oai:DiVA.org:umu-63721DiVA: diva2:582483