Heavy tailed calibration model with Berkson measurement errors for replicated data

Abstract

This work considers the so called controlled calibration model in which the independent variable is a controlled variable (Berkson type) and assumes that the measurement errors follow a scale mixtures of normal (SMN) distribution. The SMN family of distributions is an attractive class of symmetric distributions including the normal, Student-t, slash and contaminated normal distributions as special cases, providing a robust alternative to estimation in controlled calibration models in the absence of normality. An EM-type algorithm is developed, which is used to develop the local influence approach to assess the robustness aspects of the parameter estimates under four perturbation schemes. Results obtained from a real dataset in the area of chemistry are reported.