Empirical Bayes estimators for high-dimensional sparse vectors
نویسندگان
چکیده
منابع مشابه
Empirical Bayes Estimators for High-Dimensional Sparse Vectors
The problem of estimating a high-dimensional sparse vector θ ∈ R from an observation in i.i.d. Gaussian noise is considered. The performance is measured using squared-error loss. An empirical Bayes shrinkage estimator, derived using a Bernoulli-Gaussian prior, is analyzed and compared with the well-known soft-thresholding estimator. We obtain concentration inequalities for the Stein’s unbiased ...
متن کاملEmpirical Bayes Estimators with Uncertainty Measures for NEF-QVF Populations
The paper proposes empirical Bayes (EB) estimators for simultaneous estimation of means in the natural exponential family (NEF) with quadratic variance functions (QVF) models. Morris (1982, 1983a) characterized the NEF-QVF distributions which include among others the binomial, Poisson and normal distributions. In addition to the EB estimators, we provide approximations to the MSE’s of t...
متن کاملEmpirical Bayes Estimators for Borel { TannerDistributionGeorge
The Borel-Tanner probability distribution was derived by Borel (1942) and Tanner (1953) to characterize the distribution behavior of the number of customers served in a queuing system with Poisson input and constant service time. Later this probability distribution was applied in some models for random trees and branching processes. In the latter case one of the parameters can be interpreted as...
متن کاملClassification of sparse high-dimensional vectors.
We study the problem of classification of d-dimensional vectors into two classes (one of which is 'pure noise') based on a training sample of size m. The main specific feature is that the dimension d can be very large. We suppose that the difference between the distribution of the population and that of the noise is only in a shift, which is a sparse vector. For Gaussian noise, fixed sample siz...
متن کاملSparse Empirical Bayes Analysis (SEBA)
We consider a joint processing of n independent sparse regression problems. Each is based on a sample (yi1, xi1) . . . , (yim, xim) of m i.i.d. observations from yi1 = x T i1βi+εi1, yi1 ∈ R, xi1 ∈ R, i = 1, . . . , n, and εi1 ∼ N(0, σ), say. p is large enough so that the empirical risk minimizer is not consistent. We consider three possible extensions of the lasso estimator to deal with this pr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Information and Inference: A Journal of the IMA
سال: 2019
ISSN: 2049-8764,2049-8772
DOI: 10.1093/imaiai/iaz001