Motivated by the analysis of a Positron Emission Tomography (PET) imaging
data considered in Bowen et al. (2012), we introduce a semiparametric
topographical mixture model able to capture the characteristics of dichotomous
shifted response-type experiments. We propose a local estimation procedure,
based on the symmetry of the local noise, for the proportion and locations
functions involved in the proposed model. We establish under mild conditions
the minimax properties and asymptotic normality of our estimators when Monte
Carlo simulations are conducted to examine their finite sample performance.
Finally a statistical analysis of the PET imaging data in Bowen et al. (2012)
is illustrated for the proposed method.Comment: 19 figure