zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Calibration and empirical Bayes variable selection. (English) Zbl 1029.62008
Summary: For the problem of variable selection for the normal linear model, selection criteria such as AIC, $C_p$, BIC and RIC have fixed dimensionality penalties. Such criteria are shown to correspond to selection of maximum posterior models under implicit hyperparameter choices for a particular hierarchical Bayes formulation. Based on this calibration, we propose empirical Bayes selection criteria that use hyperparameter estimates instead of fixed choices. For obtaining these estimates, both marginal and conditional maximum likelihood methods are considered. As opposed to traditional fixed penalty criteria, these empirical Bayes criteria have dimensionality penalities that depend on the data. Their performance is seen to approximate adaptively the performance of the best fixed-penalty criterion across a variety of orthogonal and nonorthogonal set-ups, including wavelet regression. Empirical Bayes shrinkage estimators of the selected coefficients are also proposed.

62C12Empirical decision procedures; empirical Bayes procedures
Full Text: DOI