Statistical Inference on Memory Structure of Processes and Its Applications to Information Theory
Technical Report,15 May 2014,14 Feb 2015
University of Kansas Lawrence United States
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The research considered the application of context set models in information theory, and focused on constructing a universal code for this model class. Three areas were investigated. First, new memory models of discrete-time and finitely-valued information sources are introduced and a universal code for the new model class is presented. An algorithm is developed to compute the code, and its practical polynomial computational and storage complexities are proved. Second, a statistical method is developed to estimate the memory depth of discrete-time and continuously-valued times series from a sample. A practical algorithm to compute the estimator is a work in progress. Third, finitely-valued spatial processes on a d-dimensional integer lattice were considered, which are natural models of images. The open problem of statistical estimation of the spatial memory structure from a single observation of the process in a finite window has been solved.
- Statistics and Probability
- Information Science