Just Identified Indirect Inference Estimator: Accurate Inference through Bias Correction

Abstract

An important challenge in statistical analysis lies in controlling the estimation bias when handling the ever-increasing data size and model complexity of modern data settings. In this paper, we propose a reliable estimation and inference approach for parametric models based on the Just Identified iNdirect Inference estimator (JINI). The key advantage of our approach is that it allows to construct a consistent estimator in a simple manner, while providing strong bias correction guarantees that lead to accurate inference. Our approach is particularly useful for complex parametric models, as it allows to bypass the analytical and computational difficulties (e.g., due to intractable estimating equation) typically encountered in standard procedures. The properties of JINI (including consistency, asymptotic normality, and its bias correction property) are also studied when the parameter dimension is allowed to diverge, which provide the theoretical foundation to explain the advantageous performance of JINI in increasing dimensional covariates settings. Our simulations and an alcohol consumption data analysis highlight the practical usefulness and excellent performance of JINI when data present features (e.g., misclassification, rounding) as well as in robust estimation.