The Sampling Distribution of the W Estimator of the Number of Valid Signatures on a Petition

• Activity Number: 299
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Mark E. Eakin*+ and Mary M. Whiteside
• Companies: The University of Texas at Arlington and The University of Texas at Arlington
• Keywords: Validating signatures ; Classes in finite population ; PMF of W

Abstract

The authors recently introduced W; a new nonlinear estimator for the number of valid, unique signatures on a petition; which was better, for the cases enumerated and under a condition of zero covariance, than the popular Goodman type statistic (Whiteside and Eakin, 2008). This paper extends those results by developing the exact probability mass function of W and close approximations of the mean and variance. A signature on a petition will not be counted for two general reasons: (1) the signature is duplicated elsewhere on the petition, (2) the signer is not a registered voter, the address is nonexistent, or some such error. We will refer to signatures under (1) above as "duplicates" and those under (2) as "invalids." For a pair of identical signatures, one signature will be designated an "original" (which will be counted if otherwise valid) and one a "duplicate" (which will not be).