Title page for ETD etd-07262002-104720


Type of Document Dissertation
Author Otieno, Bennett Sango
Author's Email Address sango@vt.edu
URN etd-07262002-104720
Title An Alternative Estimate Of Preferred Direction For Circular Data
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Anderson-Cook, Christine M. Committee Chair
Prins, Samantha C. Bates Committee Member
Smith, Eric P. Committee Member
Terrell, George R. Committee Member
Ye, Keying Committee Member
Keywords
  • Preferred Direction
  • Circular Data
  • Hodges-Lehmann Estimator
Date of Defense 2002-07-25
Availability unrestricted
Abstract
Circular or Angular data occur in many fields of applied statistics. A common problem of interest in circular data is estimating a preferred direction and its corresponding distribution. This problem is complicated by the so-called wrap-around effect, which exists because there is no minimum or maximum on the circle. The usual statistics employed for linear data are inappropriate for directional data, as they do not account for the circular nature of directional data. Common choices for summarizing the preferred direction are the sample circular mean, and sample circular median. A newly proposed circular analog of the Hodges-Lehmann estimator is proposed, as an alternative estimate of preferred direction. The new measure of preferred direction is a robust compromise between circular mean and circular median. Theoretical results show that the new measure of preferred direction is asymptotically more efficient than the circular median and that its asymptotic efficiency relative to the circular mean is quite comparable. Descriptions of how to use the methods for constructing confidence intervals and testing hypotheses are provided. Simulation results demonstrate the relative strengths and weaknesses of the new approach for a variety of distributions.
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