Heavy tailed calibration model with Berkson measurement errors for replicated data

• A calibration model with Berkson-type measurement error for replicated data is proposed assuming the scale mixtures of normal distributions.
• It was developed the local infuence method to asses the robustness aspects of the parameter estimates under four perturbation schemes.
• Real data set from chemical analysis process are used to show the usefulness of our approach.

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.