JSM 2004 - Toronto

Abstract #301129

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Activity Number: 116
Type: Contributed
Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
Sponsor: General Methodology
Abstract - #301129
Title: Orthogonal Regression by Unitary Transformations
Author(s): Jonathon Schuler*+ and James E. Gentle
Companies: Naval Research Laboratory and George Mason University
Address: Optical Sciences Division / Code 5661, Washington, DC, 20375,
Keywords: robust ; orthogonal ; regression
Abstract:

This paper revisits and generalizes a published technique (1988), a routine for converting regression algorithms into corresponding orthogonal regression algorithms, that implemented orthogonal regression of two variables by determining a unitary rotation of variables such that the regression slope of the transformed variables became zero; subsequent derotation of this zero-slope regression axis corresponded to the orthogonal regression of the original variables. This paper extends the technique to the case of hyperplane surfaces resulting from the regression of three or more variables, particularly when some variables are assumed to admit measurement errors while others are known to not. This generalized approach leverages the use of any robust ordinary regression algorithm under any error metric, offering specific advantages in performance over the Total Least Squares approaches of orthogonal regression when there are deviations from the assumption of error independence and homoscedasticity.

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