Beyond Thresholding: Analysis and Improvements for Deterministic Parameter Estimation

Details Beyond Thresholding: Analysis and Improvements for Deterministic Parameter Estimation Beyond Thresholding: Analysis and Improvements for Deterministic Parameter Estimation

2008-01-23

arxiv.org/abs/0801.3490v1

Mathematics

Statistics Theory

18 pages, 11 figures

Scientific paper

Hard-threshold estimators are popular in signal processing applications. We provide a detailed study of using hard-threshold estimators for estimating an unknown deterministic signal when additive white Gaussian noise corrupts observations. The analysis, depending heavily on Cram{\'e}r-Rao bounds, motivates piecewise-linear estimation as a simple improvement to hard thresholding. We compare the performance of two piecewise-linear estimators to a hard-threshold estimator. When either piecewise-linear estimator is optimized for the decay rate of the basis coefficients, its performance is better than the best possible with hard thresholding.

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