A GENERALIZATION OF THE LINEAR RANK STATISTIC AND ITS PROPERTIES

• Main Author: ULRICH, GARY JOSEPH
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-1980
• Subjects: Statistics
• ISBN: 9798660381614

A major thrust in the area of nonparametric statistics is the testing of equality of two or more distributions, with special emphasis on the location and/or scale shift problem. The easiest and most commonly used test in the location/scale problem is the Linear Rank Statistic (LRS). Weaknesses of the LRS have been well documented and many competitors have been advanced to fill these voids. Because of the known strengths of the LRS it is logical to simply attempt to generalize the test in such a way to cover its own weaknesses. A generalization of the Linear Rank test, referred to as the Bilinear Rank Statistic (BRS), is proposed in this dissertation. A motivation for this particular generalization is provided and the BRS is shown to be a logical alternative to the LRS. Small sample moments are derived and the BRS is also shown to be Asymptotically Normal. For asymptotic comparison of the BRS and LRS, the exact Bahadur slope is shown to exist for the BRS and a method of computation is outlined. Optimality results are derived for the BRS and are used to obtain effective members of the class of Bilinear Rank tests. These tests are shown to be competitive with LRS tests that are available by performing small sample Monte Carlo power studies as well as calculating Bahadur efficiencies.