Showing papers by "Robert Tibshirani published in 1988"

Estimating Transformations for Regression via Additivity and Variance Stabilization

Abstract: I propose a method for the nonparametric estimation of transformations for regression. It is much more flexible than the familiar Box-Cox procedure, allowing general smooth transformations of the variables, and is similar to the ACE (alternating conditional expectation) algorithm of Breiman and Friedman (1985). The ACE procedure uses scatterplot smoothers in an iterative fashion to find the maximally correlated transformations of the variables. Like ACE, my proposal can incorporate continuous, categorical, or periodic variables, or any mixture of these types. The method differs from ACE in that it uses a (nonparametric) variance-stabilizing transformation for the response variable. The technique seems to alleviate many of the anomalies that ACE suffers with regression data, including the inability to reproduce model transformations and sensitivity to the marginal distribution of the predictors. I provide several examples, including an analysis of the “brain and body weight” data and some data on ...

Variance stabilization and the bootstrap

Abstract: SUMMARY We investigate the use of a variance stabilizing transformation for the computation of a bootstrap t confidence interval. The transformation is estimated in an 'automatic' manner through an initial bootstrap step. A bootstrap t interval is then computed for the variance stabilized parameter and the interval is mapped back to the original scale. The resultant procedure is second-order correct in some settings, invariant and in a number of examples it performs better than the usual untransformed bootstrap t interval. It also requires far less computation. The new interval is compared with Efron's BCa procedure and the two methods are seen to produce similar results.