Efficient Estimation for Longitudinal Data by Combining High-Dimensional Moment Conditions

• Activity Number: 156
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Korean International Statistical Society
• Author(s): Hyunkeun Cho* and Annie Qu
• Companies: Western Michigan University and University of Illinois at Urbana-Champaign
• Keywords: Bayesian information criterion ; Generalized method of moments ; Longitudinal data ; Moment selection ; Principal components ; Quadratic inference function

Abstract

The quadratic inference function approach (Qu, Lindsay and Li, 2000) is able to provide a consistent and efficient estimator if valid moment conditions are available. However, the QIF estimator is unstable when the dimension of moment conditions is large compared to the sample size, due to the singularity problem for the estimated weighting matrix. We propose a new estimation procedure which combines all valid moment conditions optimally via the spectral decomposition of the weighting matrix. In theory, we show that the proposed method yields a consistent and efficient estimator which follows an asymptotic normal distribution. In addition, Monte Carlo studies indicate that the proposed method performs well in the sense of reducing bias and improving estimation efficiency. A real data example of Fortune 500 companies is used to compare the performance of the new method with existing methods.