This proposal concerns an extention of the lossless Lempel-Ziv data compression algorithm to lossy algorithm using a rate- distortion type of fidelity criterion. The project will focus on three problems first, all related to data compression algorithm and estimation algorithms based on log convex functions: Identificattion of Log-Convex Parameters. Extension of Rissanen's Approach to the Estimation Problem. An Extimation Algorithm Motivated by the Lempel-Ziv Data Compression Algorithm. If possible, other work on data compression algorithms based on the Lempel-Ziv algorithm and modifications will be extended.//
