Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 2, 292--305

Variations on a Theme by Neyman and Pearson

V.S. Borkar , Tata Institute of Fundamental Research, Mumbai, INDIA

S.K. Mitter , Laboratory for Information and Decision Systems, Cambridge, USA

S.R. Venkatesh , Boston University, Boston, USA

SUMMARY. A symmetric version of the Neyman-Pearson test is developed for discriminating between sets of hypotheses and is extended to encompass a new formulation of the problem of parameter estimation based on finite data sets. Such problems can arise in distributed sensing and localization problems in sensor networks, where sensor data must be compressed to account for communication constraints. In this setting it is natural to focus on methods that balance coarse resolution of the estimates for achieving higher reliability.

AMS (1991) subject classification. 62F03, 62C20.

Key words and phrases. Multiple hypothesis testing, parametric inference, minmax, convex optimization.

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