Maximum Likelihood Estimation of Misspecified Models

Key Points

• This research investigates how model misspecification affects estimation and inference using maximum likelihood techniques.
• Analyzed the quasi-maximum likelihood estimator for its properties regarding convergence and consistency.
• Assessed the validity of standard tests like Wald and Likelihood Ratio in the context of model misspecification.
• Developed alternative statistics for making robust inferences despite misspecification.
• The quasi-maximum likelihood estimator converges to a defined limit but may lack consistency for certain parameters.
• Standard tests were found to be invalid when model misspecification occurs.
• Introduced new tests that leverage properties of the information matrix to robustly detect model misspecification.

Abstract