Type of Document 
Dissertation 
Author 
Otieno, Bennett Sango

Author's Email Address 
sango@vt.edu 
URN 
etd07262002104720 
Title 
An Alternative Estimate Of Preferred
Direction For Circular Data 
Degree 
PhD 
Department 
Statistics 
Advisory Committee 
Advisor Name 
Title 
AndersonCook, 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
 HodgesLehmann Estimator

Date of Defense 
20020725 
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 socalled wraparound 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 HodgesLehmann 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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