Characterizing Sums of Squares by Their Distributions

Characterizing Sums of Squares by Their Distributions

In a linear model under normality it is shown that the error sum of squares is characterized by its distribution. Two proofs are presented, one using the almost-sure uniqueness of uniformly minimum variance unbiased estimators and the other using linear algebra. Two illustrations of how this charact...

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Veröffentlicht in:The American statistician 1997-02, Vol.51 (1), p.55-58
Hauptverfasser: Seely, Justus F., Birkes, David, Lee, Youngjo
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Chi-squared distribution
College professors
Continuous functions
Covariance matrices
Degrees of freedom
Distribution theory
Error sum of squares
Exact sciences and technology
Least squares
Linear algebra
Linear hypothesis
Linear model
Linear models
Mathematical analysis
Mathematical models
Mathematical theorems
Mathematical vectors
Mathematics
Matrices
Probability and statistics
Sciences and techniques of general use
Statistical inference
Statistical variance
Statistics
Teacher's Corner
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Beschreibung
Zusammenfassung:In a linear model under normality it is shown that the error sum of squares is characterized by its distribution. Two proofs are presented, one using the almost-sure uniqueness of uniformly minimum variance unbiased estimators and the other using linear algebra. Two illustrations of how this characterization can be used are given.
ISSN:0003-1305
1537-2731
DOI:10.1080/00031305.1997.10473590