Estimation and prediction with data quality indexes in linear regressions

Abstract

Despite many statistical applications brush the question of data quality aside, it is a fundamental concern inherent to external data collection. In this paper, data quality relates to the confidence one can have about the covariate values in a regression framework. More precisely, we study how to integrate the information of data quality given by a \((n \times p)\) -matrix, with n the number of individuals and p the number of explanatory variables. In this view, we suggest a latent variable model that drives the generation of the covariate values, and introduce a new algorithm that takes all these information into account for prediction. Our approach provides unbiased estimators of the regression coefficients, and allows to make predictions adapted to some given quality pattern. The usefulness of our procedure is illustrated through simulations and real-life applications. Kindly check and confirm whether the corresponding author is correctly identified.Yes