B1876
Title: Detection of structural breaks in non-stationary spatial random field
Authors: Pramita Bagchi - George Washington University (United States) [presenting]
Abstract: A method is proposed for investigating structural breaks in a non-stationary spatial random field observed over a regular grid. The work is in a frequency domain set-up and a statistic is proposed based on the maximal difference between local spatial spectral density with maximum taken-over locations and range of frequencies. The theoretical properties of this proposed statistic are established and it is used to construct a consistent asymptotic level $\alpha$ test for the stationarity hypothesis. Further, this statistic provides a visual tool to understand the nature of non-stationarity present in the data. This visual tool is used, called a disparity map, along with the theoretical properties of this statistic to construct a piece-wise stationary approximation of the observed random field where the pieces are rectangular regions. An initial partition is constructed using a sequential application of the proposed test for stationarity. A hierarchical clustering algorithm is then used to determine the optimal number of regions and to merge the obtained partition appropriately to produce a final partition. A computationally efficient implementation of the methodology is presented. The accuracy and performance of the proposed methods are demonstrated via extensive simulations and two case studies using climate data.
