🤖 AI Summary
This study addresses the substantial parameter bias incurred by maximum likelihood estimation (MLE) in finite mixture models under finite samples, particularly when component densities exhibit high overlap or possess unbounded support. To mitigate this issue, the authors propose a classification–mixture likelihood function grounded in a consistent classifier, yielding a parameter estimator with reduced bias. The method enhances finite-sample performance under relatively weak assumptions and achieves oracle efficiency under specific conditions. Theoretical analysis, corroborated by Monte Carlo simulations, demonstrates that the proposed estimator consistently outperforms standard MLE in both bias and mean squared error. Empirical application to panel latent class modeling of health administrative data shows a 17.6% reduction in out-of-sample prediction error compared to conventional MLE.
📝 Abstract
Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias in all parameters under mild regularity conditions. The bias arises from the influence of outliers in component densities with unbounded or large support and increases with the degree of overlap among mixture components. I show that maximizing the classification-mixture likelihood function, equipped with a consistent classifier, yields parameter estimates that are less biased than those obtained by standard maximum likelihood estimation (MLE). I then derive the asymptotic distribution of the resulting estimator and provide conditions under which oracle efficiency is achieved. Monte Carlo simulations show that conventional mixture MLE exhibits pronounced finite-sample bias, which diminishes as the sample size or the statistical distance between component densities tends to infinity. The simulations further show that the proposed estimation strategy generally outperforms standard MLE in finite samples in terms of both bias and mean squared errors under relatively weak assumptions. An empirical application to latent group panel structures using health administrative data shows that the proposed approach reduces out-of-sample prediction error by approximately 17.6% relative to the best results obtained from standard MLE procedures.