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Abstract Details

Activity Number: 135
Type: Contributed
Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #306022
Title: Estimating the Ratio of Multivariate Means
Author(s): Chand Chauhan*+ and Yvonne Zubovic
Companies: Indiana University Purdue University Fort Wayne and Indiana University Purdue University Fort Wayne
Address: 2105 E. Coliseum Blvd., Fort Wayne, IN, 46805,
Keywords: bivariate data ; confidence interval
Abstract:

Consider two correlated populations X and Y each with correlated measurements; (X1, X2) and (Y 1, Y 2), respectively with µx =( µ1, µ2), µy =( a µ1, a µ2), where a is the common ratio of bivariate means. The ratio of two means is useful when evaluating the mean interest rate paid per mean amount of credit used, or the mean amount of depreciation expense per mean amount of revenue, etc. An estimate of a based on combining two estimates of a by either using linear functions of X i, and Yi or the linear functions of ratios Y i/Xi has been previously discussed . In this paper we provide an alternative way of estimating a by combining the ratios under specific conditions. Under these conditions the authors discuss the approximate distributions of each ratio and of the statistic based on both ratios. The proposed estimation methodology can be generalized for three or more correlated measurements. The properties of the confidence interval of a based on the proposed methods have been investigated and compared with the ones based on the existing methods.


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