[Back]

U. Schneider, B. Pötscher:
"Distributional results for thresholding estimators in";
Talk: 8th World Congress in Probability and Statistics, Istanbul; 2012-07-09 - 2012-07-14.

We study the distribution of hard-, soft-, and adaptive softthresholding 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 here 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.