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

Beyond Thresholding: Analysis and Improvements for Deterministic Parameter Estimation