Homoscedastic controlled calibration model

TL;DR

This paper introduces a new calibration model where the independent variable is unobservable but has a surrogate, assuming equal variances, and uses likelihood methods for estimation and inference.

Contribution

It proposes a novel calibration model with controlled variables and equal variances, employing likelihood-based estimation and Fisher information for inference.

Findings

Simulation study shows robustness of the estimator

Confidence intervals effectively capture parameter uncertainty

Model performs well with unobservable independent variables

Abstract

In the context of the usual calibration model, we consider the case in which the independent variable is unobservable, but a pre-fixed value on its surrogate is available. Thus, considering controlled variables and assuming that the measurement errors have equal variances we propose a new calibration model. Likelihood based methodology is used to estimate the model parameters and the Fisher information matrix is used to construct a confidence interval for the unknown value of the regressor variable. A simulation study is carried out to asses the effect of the measurement error on the estimation of the parameter of interest. This new approach is illustrated with an example.