Collective Nonparametric Spectral Density Estimation with Applications in Clustering

• Activity Number: 112
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Mehdi Maadooliat* and Ying Sun
• Companies: Marquette University and King Abdullah University of Science and Technology
• Keywords: Collective estimation ; Nonparametric estimation ; Roughness penalty ; Spatial processes ; Spectral density function

Abstract

This paper develops a method for simultaneous estimation of spectral density functions (SDFs) for a collection of stationary random fields (spatial processes or time series) that share some common features. Due to the similarities among the SDFs, the log-SDF can be represented using a common set of basis functions. The basis shared by the collection of the log-SDFs is estimated as a low-dimensional manifold of a large space spanned by a pre-specified rich basis. Collective estimation approach allows pooling information and borrowing strength across SDFs to achieve better estimation efficiency. Also, each estimated spectral density has a concise representation using the coefficients of the basis expansion and these coefficients can be used for visualization, clustering, and classification purposes. Whittle pseudo-maximum likelihood approach is used to fit the model and an alternating blockwise Newton-type algorithm is developed for computation.