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Activity Number:
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608
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Type:
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Contributed
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Date/Time:
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Thursday, August 6, 2009 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #303243 |
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Title:
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The Fundamentals of Statistics for Rebuilding the Methodology of the Piecewise Regression Analysis Based on a Functionalized General Trichotomy
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Author(s):
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Ligong Chen*+ and Yongmei Chen
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Companies:
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Uniformed Services University of the Health Sciences and Uniformed Services University of the Health Science
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Address:
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Department of Preventive Medicine & Biometrics, Bethesda, MD, 20814,
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Keywords:
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Piecewise Regression Analysis ; Convergence Rate of Residuals ; Weighted Mean Threshold ; Differentiality Coefficient ; Continuity Test ; Random Correspondence
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Abstract:
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We discussed the fundamentals of Statistics and pointed out that the current methodology of the piecewise regression analysis (PRA) as well as the spline violated the fundamentals. Based on constructing random threshold variables (RTV) and convergence rates of residuals (CRR) in data iterations in regression for searching thresholds, we introduced a functionalized general trichotomic regression (FGTR) as the most general segmentation in either symmetric or asymmetric with fully parametric estimates and hypothesis. We proved a necessary condition for the two kinds of trichotomic regression analysis and proposed a weighted t-test to infer the difference between any two adjacent thresholds as a sufficient condition. A continuity test and a differentiality (or similarity) coefficient can be used to evaluate the piecewise regression models.
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