  We study the distribution of hard-, soft-, and adaptive soft-thresholding
estimators within a linear regression model where the number of parameters k
can depend on sample size n and may diverge with n. In addition to the case of
known error-variance, we define and study versions of the estimators when the
error-variance is unknown. We derive the finite-sample distribution of each
estimator and study its behavior in the large-sample limit, also investigating
the effects of having to estimate the variance when the degrees of freedom n-k
does not tend to infinity or tends to infinity very slowly. Our analysis
encompasses both the case where the estimators are tuned to perform consistent
model selection and the case where the estimators are tuned to perform
conservative model selection. Furthermore, we discuss consistency, uniform
consistency and derive the uniform convergence rate under either type of
tuning.
