A semi-local likelihood regression estimator of the proportion based on group testing data

Abstract

In this paper, we are concerned with the estimation of a proportion based on group testing data where the prevalence of a disease is observed for groups of individuals. Based on the covariates measured on all individuals in every group, we propose a local likelihood estimator of the prevalence probability as a function of the covariate. We show that the proposed estimator has an asymptotic normal distribution. Finite sample performance of the method is exhibited via some simulated examples and a real data analysis.

Keywords:

• nonparametric binary regression
• local smoothing
• local likelihood

AMS Subject Classifications:

• 62G05
• 62G20