Convergence and Asymptotic Normality for Identification of Systems with Subsystems

• Activity Number: 36 - Statistcal Theory and Uncertainty Quantification in Physical Sciences
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Long Wang* and Jingyi Zhu and James C. Spall
• Companies: Johns Hopkins University and Johns Hopkins University and Applied Physics Laboratory
• Keywords: Convergence analysis; Maximum likelihood estimators; System identification

Abstract

This paper studies a stochastic system composed of multiple subsystems, where each subsystem has a general binary or non-binary output follows a univariate exponential family distribution. The full system, on the other hand, follows another multivariate exponential family distribution, such as Gaussian and multinomial distribution. Such a system has numerous practical applications. The main fields include system reliability estimation, sensor networks, object detection, and transportation network. Using the principles of maximum likelihood estimation (MLE), this paper generalizes the prior work for the stochastic system composed of binary-only subsystems. The non-binary subsystems studied in this work not only provide a more realistic model but also present the most general case in the static settings. We provide the formal conditions for the convergence of the MLEs to the true full system and subsystem parameters. The asymptotic normalities for the MLEs and the connections to Fisher information matrices are also established, which are useful in providing the asymptotic or finite-sample confidence bounds.