A Natural Identity for Exponential Families with Applications in Multiparameter Estimation

By H. Malcolm Hudson. 1978

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Kernel Mean Shrinkage Estimators (2014, background): “mator from the Bayesian point of view and soon after inspired a considerable number of works in this direction, e.g., Efron and Morris (1972, 1973b, 1975) and later by Berger (1975), Bock (1975), and Hudson (1978). Although Stein phenomenon has been extensively studied in the statistics community, i”
The SURE-LET Approach to Image Denoising (2007, result): “A proof of a similar result can be found for instance in [162, 163].”
A unifying approach to the estimation of the conditional Akaike information in generalized linear mixed models (2014, methodology): “The proofs of the essential Theorem 3.1 and Theorem 3.2 can be done by integration by parts; see Hudson (1978) with small modifications.”
Akaike's Information Criterion, Cp and Estimators of Loss for Elliptically Symmetric Distributions (2014, background): “Unfortunately, in that case, the only context in which Stein-type identities are available is the one of exponential family (Hudson, 1978), and no transition from the linear regression model to a canonical form, as in (11), is known.”
Use of exchangeable pairs in the analysis of simulations (2004, unknown): “See Diaconis and Zabell [8] and Hudson [15] for more characterizations.”
Optimal Model Assessment, Selection, and Combination (2006, background): “Generalizations in various forms have been proposed for some exponential families (e.g., Hudson 1978).”
Image Denoising in Mixed Poisson–Gaussian Noise (2011, unknown): “A proof of a similar result can be found, for instance, in [19], [34], and [35] In practice, we obviously do not have access to the original noise-free signal .”