Improved Estimation and Uncertainty Quantification Using Monte Carlo--Based Optimization Algorithms

• Activity Number: 309
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Cong Xu*+ and Paul David Baines and Jane-Ling Wang
• Companies: UC Davis and UC Davis and UC Davis
• Keywords: Convergence criterion ; Local linear kernel smoother ; MCEM algorithm ; Stochastic optimization

Abstract

In this paper we present a novel method to obtain both improved estimates and more reliable measures of convergence for stochastic optimization algorithms such as the Monte Carlo EM (MCEM) algorithm. By characterizing a stationary point of the algorithm as the solution to a fixed point equation, we provide a parameter estimation procedure by solving for the fixed point of the update mapping. We investigate various ways to model the update mapping, including a local linear kernel smoother. This simple approach typically allows increased stability in estimating the value of the stationary point as well as providing a natural quantification of the estimation uncertainty. These uncertainty measures can then be used to construct convergence criteria that reflect the inherent randomness in the algorithm. We establish convergence properties of our modified estimator. In contrast to existing literature, our convergence results do not require the Monte Carlo sample size goes to infinity. Simulation studies are provided to illustrate the improved stability and reliability of our estimator in a variety of contexts.