Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

An Analysis of Transformations Revisited

Peter J. Bickel and Kjell A. Doksum
Journal of the American Statistical Association
Vol. 76, No. 374 (Jun., 1981), pp. 296-311
DOI: 10.2307/2287831
Stable URL: http://www.jstor.org/stable/2287831
Page Count: 16
  • Download ($14.00)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
An Analysis of Transformations Revisited
Preview not available

Abstract

Following Box and Cox (1964), we assume that a transform Zi = h(Yi, λ) of our original data {Yi} satisfies a linear model. Consistency properties of the Box-Cox estimates (MLE's) of λ and the parameters in the linear model, as well as the asymptotic variances of these estimates, are considered. We find that in some structured models such as transformed linear regression with small to moderate error variances, the asymptotic variances of the estimates of the parameters in the linear model are much larger when the transformation parameter λ is unknown than when it is known. In some unstructured models such as transformed one-way analysis of variance with moderate to large error variances, the cost of not knowing λ is moderate to small. The case where the error distribution in the linear model is not normal but actually unknown is considered, and robust methods in the presence of transformations are introduced for this case. Asymptotics and simulation results for the transformed additive two-way layout show that much is gained by this robustification of the Box-Cox methods when the ratios of the means to the error standard deviation are moderate to large. However, the performance of all Box-Cox type procedures is unstable and highly dependent on the parameters of the model in structured models with small to moderate error variances.

Page Thumbnails

  • Thumbnail: Page 
296
    296
  • Thumbnail: Page 
297
    297
  • Thumbnail: Page 
298
    298
  • Thumbnail: Page 
299
    299
  • Thumbnail: Page 
300
    300
  • Thumbnail: Page 
301
    301
  • Thumbnail: Page 
302
    302
  • Thumbnail: Page 
303
    303
  • Thumbnail: Page 
304
    304
  • Thumbnail: Page 
305
    305
  • Thumbnail: Page 
306
    306
  • Thumbnail: Page 
307
    307
  • Thumbnail: Page 
308
    308
  • Thumbnail: Page 
309
    309
  • Thumbnail: Page 
310
    310
  • Thumbnail: Page 
311
    311