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Self-Consistency: A Fundamental Concept in Statistics
Statistical Science
  • Thaddeus Tarpey, Wright State University - Main Campus
  • Bernard Flury
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The term ''self-consistency'' was introduced in 1989 by Hastie and Stuetzle to describe the property that each point on a smooth curve or surface is the mean of all points that project orthogonally onto it. We generalize this concept to self-consistent random vectors: a random vector Y is self-consistent for X if E[X|Y] = Y almost surely. This allows us to construct a unified theoretical basis for principal components, principal curves and surfaces, principal points, principal variables, principal modes of variation and other statistical methods. We provide some general results on self-consistent random variables, give examples, show relationships between the various methods, discuss a related notion of self-consistent estimators and suggest directions for future research.

Citation Information
Thaddeus Tarpey and Bernard Flury. "Self-Consistency: A Fundamental Concept in Statistics" Statistical Science Vol. 11 Iss. 3 (1996) p. 229 - 243 ISSN: 0883-4237
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