Prediction and Power Transformations when the Choice of Power is Restricted to a Finite Set
We study the family of power transformations proposed by Box and Cox (1964) when the choice of the power parameter λ is restricted to a finite set Ω<sub>R</sub>. The behavior of the Box-Cox procedure is as anticipated in two extreme cases: when the true parameter λ is an element of Ω<...
| Veröffentlicht in: | Journal of the American Statistical Association. - American Statistical Association, 1922. - 77(1982), 380, Seite 908-915 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1982
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| Zugriff auf das übergeordnete Werk: | Journal of the American Statistical Association |
| Schlagworte: | Box-Cox family Contiguity Asymptotic theory Regression Conditional median Response surface Mathematics Business Behavioral sciences Philosophy |
| Zusammenfassung: | We study the family of power transformations proposed by Box and Cox (1964) when the choice of the power parameter λ is restricted to a finite set Ω<sub>R</sub>. The behavior of the Box-Cox procedure is as anticipated in two extreme cases: when the true parameter λ is an element of Ω<sub>R</sub> and when λ is "far" from Ω<sub>R</sub>. We study the case in which λ<sub>0</sub> is "close" to Ω<sub>R</sub>, finding that the resulting methods can be very different from unrestricted maximum likelihood and that inferences may depend on the design, the values of the regression parameters, and the distance of λ to Ω<sub>R</sub>. |
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| ISSN: | 1537274X |
| DOI: | 10.2307/2287326 |