The discretely observed immigration-death process : Likelihood inference and spatiotemporal applications

• We consider a stochastic process, the homogeneous spatial immigration-death (HSID) process, which is a spatial birth-death process with as building blocks (i) an immigration-death (ID) process (a continuous-time Markov chain) and (ii) a probability distribution assigning iid spatial locations to all events. For the ID process, we derive the likelihood function, reduce the likelihood estimation problem to one dimension, and prove consistency and asymptotic normality for the maximum likelihood estimators (MLEs) under a discrete sampling scheme. We additionally prove consistency for the MLEs of HSID processes. In connection to the growth-interaction process, which has a HSID process as basis, we also fit HSID processes to Scots pine data.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

LANTBRUKSVETENSKAPER  -- Lantbruksvetenskap, skogsbruk och fiske -- Skogsvetenskap (hsv//swe)

AGRICULTURAL SCIENCES  -- Agriculture, Forestry and Fisheries -- Forest Science (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Biologi -- Ekologi (hsv//swe)

NATURAL SCIENCES  -- Biological Sciences -- Ecology (hsv//eng)

Keyword

Asymptotic normality

Consistency

Homogenous spatial immigration-death process

Maximum likelihood

Spatial birth–death process

Spatiotemporal growth-interaction process

matematisk statistik

Mathematical Statistics

Publication and Content Type

ref (subject category)

art (subject category)