论文信息 - Asymptotic Solutions of the Compound Decision Problem for Two Completely Specified Distributions

Asymptotic Solutions of the Compound Decision Problem for Two Completely Specified Distributions

A compound decision problem consists of the simultaneous consideration of n decision problems having identical formal structure. Decision functions are allowed to depend on the data from all n components. The risk is taken to be the average of the resulting risks in the component problems. A heuristic argument for the existence of good asymptotic solutions was given by Robbins ([1] Sec. 6) and was preceded by an example (component decisions between N(-1,1) and N(1,1)) exhibiting, for sufficiently large n, a decision function whose risk was uniformly close to the envelope risk function of “simple” decision functions.

H. Robbins | J. Hannan

[1] L. J. Savage,et al. Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics , 1949 .

[2] Recherches théoriques modernes sur le calcul des probabilités. I: Généralités sur les Probabilités. Eléments aléatoires , 1951 .

[3] On $\epsilon$-Complete Classes of Decision Functions , 1951 .

[4] W. R. Buckland,et al. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. , 1952 .

[5] James Hannan,et al. Asymptotic solutions of compound decision problems , 1953 .