Optimal data collection design in machine learning: the case of the fixed effects generalized least squares panel data model

Abstract This work belongs to the strand of literature that combines machine learning, optimization, and econometrics. The aim is optimize data collection process in a specific statistical model, commonly used econometrics, employing an optimization criterion inspired by namely, generalization error conditioned on training input data. More specifically, paper focused analysis conditional Fixed Effects Generalized Least Squares (FEGLS) panel i.e., linear regression model with applications several fields, able represent unobserved heterogeneity associated different units, for which distinct observations related same unit are corrupted correlated measurement errors. framework considered this differs from classical FEGLS additional possibility controlling variance output variable given variables, changing cost per supervision each example. Assuming upper bound total cost, whole set, trade-off between set size precision (i.e., reciprocal variable) analyzed optimized. achieved formulating solving closed form suitable problems, based large-sample approximations estimates parameters, results extend case various its ones obtained authors recent works simpler models. They highlight importance how scales respect example determining optimal precision. Numerical confirm validity theoretical findings.