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Graphical methods for investigating the finite-sample properties of confidence regions

By Christian de Peretti and Carole Siani

Abstract

No satisfactory method for measuring and presenting the performance of confidence regions can be found in the literature. Techniques for measuring the effectiveness of confidence regions and for the graphical display of simulation evidence regarding the coverage and effectiveness of confidence regions are developed and illustrated. Three types of figures are discussed: called coverage plots, coverage discrepancy plots, and coverage effectiveness curves, which makes it possible to show the "genuine" effectiveness, rather than a spurious nominal effectiveness. These figures are used to illustrate the finite sample properties of autoregressive parameter confidence regions in the context of AR(1) processes.

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