Hierarchical models are extensively studied and widely used in statistics and many other scientific areas. They provide an effective tool for combining information from similar resources and achieving partial pooling of inference. Since the seminal work by James and Stein (1961) and Stein (1962), shrinkage estimation has become one major focus for hierarchical models. For the homoscedastic norm...

This paper discusses the properties of certain risk estimators recently proposed to choose regularization parameters in ill-posed problems. A simple approach is Stein’s unbiased risk estimator (SURE), which estimates the risk in the data space, while a recent modification (GSURE) estimates the risk in the space of the unknown variable. It seems intuitive that the latter is more appropriate for ...

Image acquisition systems invariably introduce blur, which necessitates the use of deblurring algorithms for image restoration. Restoration techniques involving regularization require appropriate selection of the regularization parameter that controls the quality of the restored result. We focus on the problem of automatic adjustment of this parameter for nonlinear image restoration using analy...

1 Stein’s lemma • In a landmark paper, Stein (1981) derived a beautiful and simple lemma about the standard normal distribution. Indeed, Stein knew of this result much earlier and wrote about it in previous papers, but in Stein (1981), the author developed a multivariate extension of this lemma that led to a remarkable result on unbiased risk estimation. (And, an interesting note: the paper Ste...

We use household survey data to construct a direct measure of absolute risk aversion based on the maximum price a consumer is willing to pay to buy a risky asset. We relate this measure to a set of consumers’ decisions that in theory should vary with attitude towards risk. We ...nd that elicited risk aversion has considerable predictive power for a number of key household decisions such as choi...

The wavelet shrinkage denoising approach is able to maintain local regularity of a signal while suppressing noise. However, the conventional wavelet shrinkage based methods are not time-scale adaptive to track the local time-scale variation. In this paper, a new time-scale adaptive denoising method for deterministic signal estimation is presented, based on the wavelet shrinkage. A class of smoo...

We address the problem of speech enhancement using a riskestimation approach. In particular, we propose the use the Stein’s unbiased risk estimator (SURE) for solving the problem. The need for a suitable finite-sample risk estimator arises because the actual risks invariably depend on the unknown ground truth. We consider the popular mean-squared error (MSE) criterion first, and then compare it...

A cross-sectional study evaluated 182 students in the last two years of medical school and 70 residents of a national hospital in Peru on the risk indicators used for reporting results in clinical trials. A questionnaire was used to assess the ability to recognize and calculate risk indicators most widely used in the epidemiological literature. From the participants, 19.4% did not recognize any...

SURE-LET Approach is used for reducing or removing noise in brain Magnetic Resonance Images (MRI). Removing or reducing noise is an active research area in image processing. Rician noise is the dominant noise in MRIs. Due to this type of noise, the abnormal tissue (cancerous tissue) may be misclassified as normal tissue and introduces bias into MRI measurements that can have significant impact ...