  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.
