Statistical inference for Gibbs point processes based on field observations

Abstract

Forest inventories are mostly based on field observations, and complete records of spatial tree coordinates are seldom taken. The lack of individual coordinates prevents the use of well stablised statistical inference tools based on the likelihood function. However, the Takacs–Fiksel approach, based on equating two expectations derived from different measures, can be used routinely without any measurement of tree coordinates, just by considering nearest neighbour measurements and the counting of trees at some random positions. Despite this, little attention has been paid to the Takacs–Fiksel method in terms of the type of test function and the type of field observation data considered. Motivated by problems based on field observations, we present a simulation study to analyse and illustrate the quality of the parameter estimates for this estimation approach under distinct simulated scenarios, where several test functions and distinct forest sampling designs are taken into account. Indeed, the type of the chosen test function affects the resulting estimates in terms of the forest field observation considered.