Sammanfattning

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

Nyckelord

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

Publicerad i

Research report (Centre of Biostochastics)
2010, nummer: 2010:01, sidor: 1-53
Utgivare: Centre of Biostochastics, Swedish University of Agricultural Sciences

SLU författare

• Yu, Jun

  • Institutionen för skogsekonomi, Sveriges lantbruksuniversitet
    

UKÄ forskningsämne

Skogsvetenskap


Permanent länk till denna sida (URI)

https://res.slu.se/id/publ/29334