Title: A rational approach to inference on multiple parameters
Authors: Brigham Frandsen - Brigham Young University (United States) [presenting]
Abstract: An approach is proposed to inference on multiple parameters that produces valid simultaneous inferences on multiple parameters while maintaining precision on the parameter or parameters of greatest interest. The approach allows inference to reflect differing preferences for precision that the researcher may have across parameters, resulting in hypothesis tests that are more powerful and confidence regions with shorter projections on the parameters that the researcher cares more about, while remaining jointly valid across all parameters. A researcher using the procedure specifies in advance non-negative weights that correspond to the relative preference for precision across parameters. The proposed confidence procedure chooses a confidence region to minimize the weighted sum of the projections on the parameter dimensions. A decision theoretic framework presents axioms for researcher preferences under which the proposed procedure is optimal.