Trading Bias for Precision: Decision Theory for Intervals and Sets
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Abstract:
Interval- and set-valued decisions are an essential part of statistical inference. Despite this, the justification behind them is often unclear, leading in practice to a great deal of confusion about exactly what is being presented. In this paper we review and attempt to unify several competing methods of interval-construction, within a formal decision-theoretic framework. The result is a new emphasis on interval-estimation as a distinct goal, and not as an afterthought to point estimation. We also see that representing intervals as trade-offs between measures of precision and bias unifies many existing approaches -- as well as suggesting interpretable criteria to calibrate this trade-off. The novel statistical arguments produced allow many extensions, and we apply these to resolve several outstanding areas of disagreement between Bayesians and frequentists.
Subject Area:
Statistical Theory and Methods
Suggested Citation:
Kenneth M. Rice, Thomas Lumley, and Adam A. Szpiro, "Trading Bias for Precision: Decision Theory for Intervals and Sets" (August 11, 2008). UW Biostatistics Working Paper Series. Working Paper 336.
http://www.bepress.com/uwbiostat/paper336