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A non-parametric analysis of transformations. (English) Zbl 0649.62037
A non-parametric estimator is proposed for the transformation model, where, following {\it G. E. P. Box} and {\it D. R. Cases tables are also provided for specific values of $\epsilon$, and the joint confidence coefficient 1-$\alpha$. For the general case, a method to compute the sample size is developed resulting in an integral equation involving the covariance matrix. In case a prior estimate of the covariance matrix is available, the integral equation can be solved by using the algorithm given by {\it N. S. Russell}}, {\it D. R. Farrier} and {\it J. Howell}, J. R. Stat. Soc., Ser. C 34, 49-53 (1985; Zbl 0571.60023). Examples are used to illustrate the effects of dimensions and quality of prior estimates of covariance matrices on the sample size.

MSC:
62G05Nonparametric estimation
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References:
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