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

Tommy Wright

KEY WORDS:

Accuracy, Maximum Ratio, Test of Unacceptability

ABSTRACT

A common practice of a national statistical agency (and most scientific investigations) is to assess its estimate for a particular real-valued characteristic (parameter) by comparing it to competing estimates from other sources. The nature of the assessment is to explain the differences. While assessing the quality of energy estimates (e.g., reserves, production, supply, sales, consumption,...), 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 targeted real-valued parameter. In this paper, we (1) provide a visual proof of the (Main Result), (2) present a test of unacceptability for at least one of the competing estimates using the maximum ratio, (3) give an application assessing the national count from the 2010 U.S. Census, and (4) extend the maximum ratio and statement to vector-valued parameters. The test can be applied in any situation where several measurements of the same phenomenon exist and one wants to quantify with certainty how far away from the truth at least one of the estimates is. Even if all estimates are near each other, this does not necessarily imply that they are near the unknown true value. The test sends a signal calling for further investigation when a pre-set standard is exceeded.

CITATION:

Tommy Wright. (2013). A Visual Proof, a Test, and an Extension of a Simple Tool for Comparing Competing Estimates. Center for Statistical Research & Methodology, Research and Methodology Directorate Research Report Series (Statistics #2013-05). U.S. Census Bureau. Available online at <http://www.census.gov/srd/papers/pdf/rrs2013-05.pdf>.

Source: U.S. Census Bureau, Center for Statistical Research & Methodology, Research and Methodology Directorate

Published online: September 10, 2013
Last revised: February 23, 2014

 


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Source: U.S. Census Bureau | Research and Methodology Directorate | Center for Statistical Research & Methodology | (301) 763-3215 (or chad.eric.russell@census.gov) |   Last Revised: February 24, 2014