2001
DOI: 10.1198/016214501753208753
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Estimation for the Box-Cox Transformation Model Without Assuming Parametric Error Distribution

Abstract: Box and Cox proposed a power transformation for the response variable that yields a linear regression model with normal error and constant variance. Inference procedures for the regression coef cients and transformation parameter under this model setting have been studied extensively. In this article we propose a simple semiparametric estimation method for the Box-Cox transformation model with no speci c parametric assumption on the distribution of the error term. The resulting estimators are strongly consiste… Show more

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Cited by 39 publications
(46 citation statements)
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“…The justification is given in the Appendix B. This resampling method is a special version of bootstrap method and has been successfully used in various settings [Foster et al, 2001, Jin et al, 2001. Compared with the conventional bootstrap, the independence between the random weights B i s simplifies the theoretical justification.…”
Section: Point Estimator and Numeric Algorithmmentioning
confidence: 99%
“…The justification is given in the Appendix B. This resampling method is a special version of bootstrap method and has been successfully used in various settings [Foster et al, 2001, Jin et al, 2001. Compared with the conventional bootstrap, the independence between the random weights B i s simplifies the theoretical justification.…”
Section: Point Estimator and Numeric Algorithmmentioning
confidence: 99%
“…That is, it should be introduced a procedure for looking for the transformation parameters. Since our aim is to study the generalization performance of the model, the proposal is to get the transformations in the BoxCox family that minimize the gh-prediction error, that is min k1,k2 We introduce a standard grid search method in this context (see, for example, Foster et al, 2001). The grid is usually defined by a multidimensional array (in our case we use two dimensions).…”
Section: Fitting the Parameters Of The Box-cox Transformationsmentioning
confidence: 99%
“…In practice, the parametric power transform proposed by Box and Cox 6 is the most used in the linear regression model context. In the literature there are many works dealing with this kind of problem (see, for example, Scallan et al, 29 Edwards and Hamilton, 17 Foster et al, 21 Marazzi and Yohai, 27 Hamasaki and Kim 23 ). This approach is used in order to adjust data to a linear regression model.…”
mentioning
confidence: 99%
“…Foster, Tian, and Wei (2001) show the identifiability of θ 0 in cases in which the disturbance U is known to be independent of the explanatory variable X. Apart from independence, the remaining requirements of Foster, Tian, and Wei's (2001) result are fairly weak: β 0 X is assumed to take at least two possible values (which excludes the case β 0 = 0), and the unknown distribution of U is assumed to have mean 0. However, in applications in which the endogeneity of U is suspected, the independence assumptions between U and X typically fail.…”
Section: Introductionmentioning
confidence: 99%