Asymptotic bias of the hazard probability model under model mis-specification

Abstract

We compare the sensitivity of the estimated effective strip half-width with respect to choice of hazard probability function (Q). This is done by fitting the model under an erroneous assumption about the parametric form of Q, and comparing the estimated and true effective strip half-width. An ‘infinite sample size’ setting is employed, where fitting the model by maximum likelihood amounts to minimising the Kullback Leibler distance between the assumed and true models. The experiment is carried out in a situation that is relevant to minke whale sighting surveys both in the Antarctic and in the northeastern Atlantic. It is found that the hazard probability model is fairly robust with respect to the choice of parametric class for Q. The largest observed bias in the resulting effective strip half-width is less than 10%, while for most situations there is almost no bias.