Sequential universal compression for binary sequences with constrained distributions

Two low-complexity methods are proposed for sequential probability assignment for binary i.i.d. individual sequences with empirical distributions whose governing parameters are known to be bounded within a limited interval. The methods can be applied to different problems where fast accurate estimation of the maximizing sequence probability is very essential to minimizing some loss. Such applications include applications in finance, learning, channel estimation and decoding, prediction, and universal compression. The application of the new methods to universal compression is studied, and their universal coding redundancies are analyzed. One of the methods is shown to achieve the minimax redundancy within the inner region of the limited parameter interval. The other method achieves better performance on the region boundaries and is more robust numerically to outliers. Simulations support the analysis.