What Can We Do When EM Is Not Applicable? Self Consistency: A General Recipe for Semiparametric and Nonparametric Estimation with Incomplete and Irregularly Spaced Data

• Activity Number: 146
• Type: Invited
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Xiao-Li Meng*+
• Companies: Harvard University
• Keywords: Iterative Algorithm ; Multiple Imputation ; Fix-point Equation ; Wavelets

Abstract

Self-consistency principle, originated by Efron (1967), generalizes MLE for semi/non-parametric estimation with incomplete data and under an arbitrary loss function. It is conceptually appealing, essentially a mathematical formalization of the common-sense "trial-and-error" methods; mathematically elegant, with one fixed-point equation to solve and a general contraction mapping theorem to establish its optimality; and practically straightforward because it directly uses a complete-data method (e.g., LASSO, kernel density estimation) within iterations, much like the EM algorithm. Its major disadvantage is that it can be computationally very intensive. However, increasingly efficient (approximate) implementations are being discovered, such as for wavelet de-noising with hard and soft thresholding. This talk summarizes these findings, based on joint work with Thomas Lee and Zhan Li.