A Visual Proof, a Test, and an Extension of a Simple Tool for Comparing Competing Estimates

• Activity Number: 607
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Tommy Wright*+
• Companies: US Bureau of the Census/Center for Statistical Research and Methodology
• Keywords: Accuracy ; Maximum Ratio ; Test of Unacceptability

Abstract

A common practice of a national statistical agency (also most scientific investigations) is to assess its estimate for a particular real-valued parameter by comparing it to comparable estimates from other sources. The nature of the assessment is to explain the differences. For example, the national count from Census 2010 has been compared to three other estimates; one (actually five) from demographic analysis, one from the Census Bureau's Population Estimates Program, and one from a nationwide sample survey. Tsao and Wright (1983) introduced a simple tool (maximum ratio) and used it to prove a statement regarding the closeness of a set containing a particular estimate and competing estimates to the unknown true value of the real-valued parameter. In this paper, we (1) provide a visual proof of the statement, (2) present a test for using the simple tool, (3) give applications for a variety of real data, and (4) extend the simple tool and statement to vector-valued parameters.