An Improved Result Relating Quadratic Forms and Chi-Square Distributions |
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Authors: | Michael F. Driscoll |
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Affiliation: | Department of Mathematics , Arizona State University , Tempe , AZ , 85287 , USA |
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Abstract: | Results from the theory of linear models establish a particular idempotency condition as being necessary and sufficient for a quadratic form in a nonsingular normal vector to follow a chi-square distribution. We give a theorem that is somewhat stronger than the standard ones, and provide a proof that is more accessible than those usually given, in that it uses only linear algebra and calculus. |
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Keywords: | Idempotent matrices Linear models Normality |
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