Completeness, Similar Regions, and Unbiased Estimation—Part II

By Erich Leo Lehmann, H. Scheffé. 2012

210 citations recorded by the source corpus.

Subfields: Applied Mathematics, Artificial Intelligence, Statistics and Probability

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Citations in the corpus

The Ideal Continual Learner: An Agent That Never Forgets (2023, background): “In this section, we show that the Ideal Continual Learner† is sufficient (Fisher, 1922) and minimal (Lehmann & Scheffé, 1950), which are two general and fundamental properties in the information-theoretical and statistical sense.”
Linear regression (2012, unknown): “y = Xβ + ε with ε ∼ N ( 0, σ 2I ) , (2)”
Statistical inferences for stress–strength in the proportional hazard models based on progressive Type-II censored samples (2015, unknown): “Hence, by using the fact that T1 and T2 in Equations (4) and (5) are complete sufficient statistics and appealing Lehmann and Scheffë Theorem,[20] the UMVUE of R is given by”
Optimal Inference After Model Selection (2014, methodology): “In particular, the following classic result of Lehmann and Scheﬀ´e (1955) gives a simple construction of UMPU tests in exponential family models.”
Learning and generalization with the information bottleneck (2008, methodology): “The method has proven to be useful for a number of important applications (see [23, 8, 20] and references therein), but its learning theoretic justiﬁcation has remained unclear, for two main reasons: (i) The method assumes that the joint distribution of X and Y is known, and uses it explicitly.”
Causal inference with confounders missing not at random (2017, unknown): “We use the notion of bounded completeness for general X and Y , which is related to the concept of a complete statistic (Lehmann & Scheffé, 1950; Newey & Powell, 2003).”
PROBABILITY DISTRIBUTIONS WITH SUMMARY GRAPH STRUCTURE (2010, background): “The notion of completeness has been introduced and studied in quite different contexts [see Lehmann and Scheffé (1955); Brown (1986), Theorem 2.”