🤖 AI Summary
This paper addresses the bias in linear regression parameter estimation arising from misclassification errors in categorical covariates. We propose an asymptotically bias-corrected estimator that requires neither access to true covariate observations nor data recalculation. The method integrates the least-squares estimator based on noisy covariates, the marginal distribution of the true covariates, and the misclassification transition probability matrix, explicitly modeling and eliminating systematic bias induced by measurement error—particularly improving consistency of the intercept estimate. Theoretical analysis establishes the consistency and asymptotic normality of the corrected estimator. Simulation studies confirm its effectiveness across diverse misclassification structures, significantly reducing parameter bias, enhancing estimation accuracy, and increasing statistical power. The key innovation lies in achieving an analytical correction of classical linear regression estimates using only prior knowledge of the misclassification mechanism—specifically, the conditional misclassification probabilities—without requiring additional data or iterative procedures.
📝 Abstract
The objective of this work is to propose an asymptotic correction method for the estimators of parameters from regression models with covariates subject to classification errors. A correction was developed based on the least squares estimators from regression with erroneous covariates, the marginal probability of the true covariates, and the conditional probability of the erroneous covariates given the true covariates. In this way, we can correct these estimators without the need to correct the erroneous covariates or observe the true covariates. We performed simulations to quantify the performance of the proposed corrections, identifying, that correcting the intercept is crucial for a significant improvement in estimation.